The 28-year-old joined Hibs on a loan deal until the end of the season in February after a deadline-day move to Blackburn Rovers fell through.
Working again with former Hoops boss Neil Lennon, Ambrose featured 12 times as the Edinburgh side secured the Scottish Championship title.
Now, following the expiration of his Celtic contract, Ambrose has penned a two-year deal at Easter Road.
Hibernian chief executive Leeann Dempster told the club's website: "Efe is a player of real quality, and one who excited the fans when he arrived on a short-term deal.
"The club as a whole are delighted to be bringing in a player with his quality and experience.
"Neil was really keen to get Efe over the line, and we're delighted to have been able to achieve that. Bringing in a player like Efe is a coup and the supporters played their part."