Hooiveld told his new club's official website: "I'm delighted to sign for a club of Celtic's stature.
"Celtic has a magnificent history and is a club with great tradition and great supporters."
He added: "Having visited the club and spoken to the manager, I feel this is the right place for me and I am very much looking forward to meeting up with my new team-mates and hopefully playing my part in bringing success to the club and our fans."
Hoops boss Tony Mowbray said: "We are very pleased to welcome Jos to Celtic.
"He is a player who we believe can make an important contribution to the club and someone we look forward to working with."
Hooiveld helped AIK win the Swedish double in his only season with the club, who have fallen on hard times financially.
The defender failed to make the grade at first club Heerenveen and was even rejected by Livingston after a trial there in 2005.
After a loan spell at Dutch second division side FC Zwolle, he moved to Austrian side Kapfenberger SV.
The following season, he joined Finnish club Inter Turku and earned himself a move to AIK two years later.
Celtic must also consider whether to make a fresh bid for Preston defender Sean St Ledger after seeing an approach rejected by the Coca-Cola Championship club last week.
Deepdale chairman Derek Shaw said of the Republic of Ireland international: "We accept Sean wants to play at a higher level and has his international career to think of, so the ball is in Celtic's court."
Hooiveld and St Ledger would fill the void left by Gary Caldwell's impending departure.
The Hoops have agreed a fee with Middlesbrough for the sale of Scotland defender Caldwell and midfielder Barry Robson, though there have been reports of the former holding talks with Wigan.
Willo Flood and Chris Killen are also close to a reunion with former Celtic boss Gordon Strachan at the Riverside.
Meanwhile, it is understood that striker Scott McDonald - who has been linked with a move to Wigan - is due to fly to Germany for surgery on a hernia problem.
He is expected to be out for up to 10 days once he goes under the knife.
That would rule him out of Saturday's SPL game with Falkirk and possibly the Scottish Cup fourth-round tie at Morton.
The match had been rescheduled for Tuesday night but has been put back to next Monday, once again because of a frozen pitch.