The former Fulham and Bristol City centre-half becomes head coach Alan Stubbs' sixth signing of the summer transfer window.
Fontaine, 28, who was released by the Robins at the end of last season after joining the club in 2006, arrives at the Edinburgh side on the same day that fellow defender Michael Nelson left to join Cambridge United.
“I’m really excited about the move and the challenge of getting Hibs back into the Premiership,” Fontaine told the club’s website.
“There were a few factors that made me sign - the prospect of working with the manager, becoming part of a young, hungry squad and the opportunity of playing for such a big club with great supporters.
“Everything pointed towards this being the right move for me and, after spending the last eight years down at Bristol City, coming up here is a fresh challenge and one I’m looking forward to.”
Stubbs added: “I’m delighted that we’ve been able to bring Liam to the club – this is a transfer that we’ve been working on for the past two weeks.
“So it’s very pleasing that all of that hard work has come to fruition and that we’ve recruited an excellent centre-half.
“Liam is a real quality signing, who will undoubtedly add a huge amount to the squad and further strengthen our defence.
“We did our homework on him – both as a player and as a person – and he ticked all the right boxes and he has immediately bought into what we’re trying to achieve at the club.”