The 28-year-old scored three goals on loan at Tannadice last term from Brentford.
He becomes manager Alan Stubbs' second summer signing after full back David Gray joined up last week.
"As soon as I came here the move felt right and I felt good about playing for Hibs," El Alagui told the club website.
I'm thrilled he has seen the potential and, after we had a chat, he bought into my vision for Hibernian and the direction where we want to go
The Moroccan notched 18 goals during an impressive season with Falkirk in 2011-12, and will once again be playing in Scotland's second tier next term following Hibs' relegation to the Championship.
"I think the Scottish Championship will be a very exciting league next season," El Alagui said.
"I had a few other offers to consider before I chose Hibernian. I thought this was the most exciting challenge and it was very clear in my head that I wanted to be here."
Stubbs, who revealed he is hoping to bring in more new faces ahead of the start of the season, said: "We've had to fight off competition from Scottish Premiership clubs and also competed with clubs from down south in order to bring Farid here to the club.
"I'm thrilled he has seen the potential and, after we had a chat, he bought into my vision for Hibernian and the direction where we want to go."
Hibernian have signed former Dundee United and Falkirk striker Farid El Alagui on a two-year deal.