The 32-year-old German has been on trial with the Swans after leaving Red Bull Salzburg at the end of last season.
He impressed in the pre-season friendly victories over Celtic and Real Betis and has been handed a two-year contract by the south Wales club.
Tremmel told the club website: "I am delighted to be here as a Swansea player.
"I've been with the club for quite a while on trial, and I already felt part of the squad as everyone here is so welcoming. It is a family club.
"I have also had the chance to see how the team gets on in the Premier League, and I have been impressed by what I have seen."
Tremmel is the third goalkeeper to be snapped up by Rodgers following the departure of Dorus de Vries to Wolves.
Michel Vorm has made a big impression since joining from FC Utrecht, while former Benfica stopper Jose Moreira is also at the Liberty Stadium.
Youngster David Cornell, currently on loan at Hereford, is also on the club's books but Rodgers' desire to see him get regular first-team football has seen him look for a third addition between the posts.
Rodgers remains hopeful of bringing in defensive and midfield reinforcements before the transfer window shuts on Wednesday night.
Source: PA
Source: PA