A 2019 Six Nations Grand Slam winner and World Cup semi-finalist with Wales, Francis last season sealed a Gallagher Premiership and Heineken Champions Cup with Exeter Chiefs.
Francis, 28, has been capped 52 times by Wales and is a proven performer at Test and European level.
He will join the Ospreys in the summer.
Francis, said: “I spoke to the Welsh regions but I was impressed with the vision of head coach Toby Booth and where he wanted to take the Ospreys. His attention to detail and knowledge of my game and what he and Duncan Jones laid out to me was really appealing.
“Toby and the coaches there are starting to steer the ship in the right direction. It’s just an exciting challenge for myself and I can see the potential there. Off the pitch there is a new backer and it’s exciting to see where that takes the Ospreys.
“The boys I know in the Wales squad all talked positively about what is happening at the Ospreys and it seems like a place that is heading in the right direction. The Ospreys just stood out to me as the region that is going places.
“I know a lot of the boys there from the Wales set-up and the squad has some talented youngsters sprinkled with some real experience and knowledge. I know there will be real competition for the shirt and we all need that as players.
“Signing for the Ospreys will allow me to continue to play for Wales, something I was not willing to give up, but to do that I know I have to perform and earn my place with the Ospreys. Performing for the Ospreys will give me the opportunity to be selected for international rugby.
“I’m still ambitious and keen to keep improving and I see Ospreys as the perfect place to do that.”
Francis was born in York and after a stint at Doncaster he headed to Sandy Park to join Exeter.
He was first called up by Wales before the 2015 World Cup and has been a regular ever since.
“In our new era and on the journey we are on, it is important to show both ambition and a desire to develop our own players,” said Ospreys head coach Toby Booth.
“Signing a current international tighthead prop with a winning history and mentality will help the Ospreys make the steps we need to make and fuel the ambition now and for the long term future.
“Tom’s decision to join us is a great sign of the progress we are making and shows the intent and commitment to what we want to be as the Ospreys.
“He has won European and domestic honours and he will bring a wealth of experience and a massive set-piece capability to our squad. His qualities will prove invaluable going forward as we prepare for the new challenges presented by the new PRO16 competition.”
