The Browns, the worst team in the National Football League last season, traded for Osweiler and a second round draft pick, freeing up millions in cap space for the Texans.
According to Schefter, the Browns are not interested in keeping Osweiler and are likely to trade him, which would result in an NBA-like transaction in which teams trade bloated contracts to get them off the books - a rare occurrence in the NFL.
The Texans traded Osweiler, who signed a four-year, $72 million deal last year and had a wildly disappointing 2016 season, to the Browns on Thursday afternoon.
At one point in the season, during December, he was removed from the starting lineup, and was a backup for Tom Savage.
The Browns have two picks in the 1st round of the 2017 NFL Draft (#1, #12 via Eagles from QB Carson Wentz trade) and two picks in the 2nd round (#33, #52). The actual trade included second rounder and a sixth rounder in exchange for a fourth round pick from the Browns.
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Openside flanker Justin Tipuric will win his 50th cap, packing down alongside back-row colleagues Sam Warburton and Ross Moriarty. Forwards: Jack McGrath, Rory Best, Tadhg Furlong, Donnacha Ryan, Devin Toner, CJ Stander, Sean O'Brien, Jamie Heaslip.
This Osweiler trade doesn't make the Browns a guarantee to trade for Garoppolo, although they remain the Patriots best hope. It seems like he was acquired just so Cleveland could secure another draft pick. Or they can just eat that dead money now, which doesn't matter when you have more cap space then you can realistically spend, as Cleveland does now. Many reports indicated that Romo would be released today, but could Jerry Jones be changing his tune if a deal can be struck with the Texans?
Although free agency is only a day old, plenty more moves will be made, with the likes of Dallas quarterback Tony Romo expected to move teams.
Osweiler should be a cautionary tale for the Browns and those fans who still believe the team should "do anything it takes" to acquire current New England Patriots quarterback Jimmy Garoppolo.
For the Texans management, the vital thing was to change their quarterback and to find some other option at that position.
The Browns gave Griffin a chance to revive his career after he was released by the Washington Redskins following the 2015 season.