The pair spent time together at the Texas Republican Convention earlier this month, and Weber's campaign on Monday quoted Paul as saying, "I am pleased to endorse Randy Weber."
Paul chose not to seek re-election to focus on his presidential run, but has since suspended his campaign.
Paul has represented the district including his hometown of Lake Jackson for 24 years.
Weber faces a runoff July 31 with Pearland City Councilwoman Felicia Harris. That's because none of the crowded field of Republicans vying for their party's nomination for Paul's seat won a majority of the votes in last month's primary.
The winner faces Democratic former U.S. Rep. Nick Lampson in November's general election.