Miller, the Big Ten offensive player of the year in 2012 and '13, tweeted Wednesday that he had a successful follow-up visit at the office of Dr. James Andrews regarding the shoulder.
Then, in response to a question from the Columbus Dispatch about his future, he answered he would make an announcement next week.
As a recent graduate, Miller is eligible to transfer and play in 2015. But, as expected, he will remain at Ohio State and compete next month with Cardale Jones and J.T. Barrett for the starting job.
Andrews performed surgery last August to repair a torn labrum in Miller's right shoulder. In his place, Barrett started 12 games and broke Miller's single-season school record for total offense. After Barrett broke his right ankle in the regular-season finale, Jones led the Buckeyes to three wins and a national championship.
Miller and Barrett were limited in spring practice as they continued to rehab.
Ohio State coach Urban Meyer told reporters Wednesday at a youth instructional camp in Geneva, Ohio, that both quarterbacks were progressing well.
"Braxton is pretty close to full speed," Meyer said, according to Cleveland.com. And Barrett, according to the coach, is "close to 95 percent."
Ohio State opens preseason camp in early August.
Information from ESPN.com's Mitch Sherman was used in this report.
Braxton Miller plans to stay at Ohio State
Joe Schad reports the latest on Braxton Miller, who will return to play at Ohio State.