Osweiler, 25, will be joined by former Miami Dolphins running back Lamar Miller, who has agreed to a four-year, $26 million contract with the Texans, a source told Schefter. Miller, 24, will receive $14 million guaranteed, the source said.
A source also told ESPN's Adam Caplan that former Kansas City Chiefs guard/tackle Jeff Allen is expected to sign a four-year, $28 million deal with Houston.
The NFL Network first reported Osweiler's decision to jump to Houston from the defending Super Bowl champion Broncos.The decision comes two days after Manning retired from the Broncos.
As part of Osweiler's contract, he will receive $37 million guaranteed, a source told ESPN's Ed Werder.
By signing Osweiler, the Texans are seeking to improve their ruinous quarterback situation from 2015. Owner Bob McNair has more than once this offseason publicly demanded the Texans find a solution at the position, though his focus has been on the draft.
In the 2015 offseason, Houston signed Ryan Mallett and Brian Hoyer to backup quarterback-level deals, then allowed them to compete for the starting job.
Hoyer won the job but threw an interception on his first pass of the season. He was benched during the Texans' Week 1 game, and coach Bill O'Brien replaced him with Mallett as the starter for the next four games. Mallett went 1-3 and lost his job to Hoyer during his fourth start. O'Brien later said he shouldn't have benched Hoyer so quickly.
"Quarterback was our No. 1 priority," Texans owner Bob McNair told the Houston Chronicle. "[Osweiler] was the one we wanted. [General manager] Rick [Smith] said he was going to get him and he did."
Osweiler started seven games in 2015 after replacing Manning, who was recovering from a tear in his plantar fascia near his left heel, but Manning reclaimed the quarterback job for the playoff run.
The Broncos had worked diligently since their win in Super Bowl 50 to re-sign Osweiler, groomed to be the future starter since he was their second-round pick in the 2012 draft. That was the same year the Broncos signed Manning in free agency.
"We've stayed true to our philosophy of building a team with players who want to be Denver Broncos and want to be here," Broncos executive vice president and general manager John Elway said Wednesday. "That's been a successful approach for us."
"While we did offer a very competitive and fair long-term contract to Brock, we ultimately had to remain disciplined while continuing to assemble a roster that can compete for championships," Elway said.
Osweiler waited until the 2015 season to make his first regular-season starts in the NFL. Broncos coach Gary Kubiak said at the scouting combine while that extended wait might have been difficult for Osweiler, it may have helped the quarterback's game overall with a more traditional developmental approach.
Miller rushed for 872 yards and scored 10 total touchdowns last season. At times he was dynamic for the Dolphins, but too often Miller was ignored in the offense. He had six games last season with single-digit rushing attempts.
As a result, Miller failed to reach his goal of back-to-back 1,000-yard seasons heading into free agency.
"I think I did all right," Miller said after the season in January. "Of course I wanted to get 1,000 yards. That was my goal coming into this season, but that didn't happen. But I think I did a good job with my opportunities to try to help this team win and just try to make plays."
Miller put together a solid résumé the past two years as a full-time starter. He rushed for 1,971 yards and scored 19 total touchdowns in that span.
Osweiler probably spent more time with Manning over the past four seasons than any other coach or player inside the team's Dove Valley complex. Osweiler has consistently said he wanted to be a starter and believed he could be but added that he "didn't want to waste a moment of the time working with Peyton."
The Broncos were 5-2 in games Osweiler started in 2015, though he was pulled in the third quarter of the regular-season finale. Two of Osweiler's wins were overtime victories against the New England Patriots and Cincinnati Bengals, which helped the Broncos earn home-field advantage in the playoffs.
Osweiler finished the season with 1,967 yards passing, 10 touchdowns and six interceptions. He had three games with at least 296 yards passing, in losses to Oakland and Pittsburgh and the win over Cincinnati.
Perhaps the only developmental concern for Osweiler is the number of sacks he took last season. He was sacked 20 times in his starts, a span of just over 27 quarters. Osweiler was listed on the injury report over those seven starts for shoulder, rib, elbow and knee injuries.
Hoyer started nine games for the Texans last season and went 5-4. His completion percentage of 60.7 ranked 25th in the NFL, his yards per attempt of 7.06 ranked 24th, and his Total QBR ranked 19th. He threw only seven interceptions in the regular season but threw four in the Texans' 30-0 playoff loss to the Kansas City Chiefs.
In all, Houston started four quarterbacks in their 9-7 campaign, using Hoyer, Mallett and midseason pickups T.J. Yates and Brandon Weeden.
Allen, 26, is a versatile offensive lineman who started at left guard and right tackle during his four seasons with the Chiefs. A 2012 second-round draft pick out of Illinois, Allen started 13 games for the Chiefs as a rookie. When healthy, he has been in the lineup ever since.
Injuries, however, have been a problem for Allen over the past two seasons. He missed all but the season opener in 2014 because of an elbow injury and then missed four games last season because of knee and ankle problems.
ESPN's Tania Ganguli, James Walker, Jeff Legwold and Adam Teicher contributed to this report.
Why did Osweiler choose Texans over Broncos?
Adam Schefter breaks down why he thinks QB Brock Osweiler decided to sign with the Texans over the Broncos, as well as what he believes the Broncos plan will be moving forward to fill their void at quarterback.