A four-year deal with Celtic ended protracted negotiations for the Danish international, whose contract at Upton Park was up at the end of the season.
"I've always wanted to play for one of the big names in European football and the opportunity to join a club of Celtic's standing fulfils that ambition," Rieper said.
"As soon as I heard they were interested I was delighted to talk to them - it has taken quite a time but I'm pleased to be here at last.
"I'm excited at the prospect of playing in front of home crowds of over 40,000 every other match - few clubs in Europe can provide that platform combined with this magnificent stadium."
Harry Redknapp, who signed Rieper for pounds 1m from Brondby in 1994, was reluctant to lose the central defender.
"I've got a lot of time for Marc, but at the end of the day we're getting a profit overall and we have had three years out of him, so it's not a bad deal," said the Hammers manager as he wrestled with the problem of replacing the player in his side at Manchester United today. Rieper, meanwhile, will be playing Motherwell.
The 29-year-old Rieper, who was not signed in time to play in Celtic's Uefa Cup home match against Liverpool on Tuesday, is the Glasgow club's seventh new arrival of the season as they attempt to break Rangers' stranglehold on Scottish football.
Ian Pearce has been told he he can leave Blackburn Rovers but only if Crystal Palace pay pounds 3m for the 23-year-old defender's services. Palace have made two offers, neither of which have matched Rovers' valuation
Wolverhampton Wanderers have raided the GM Vauxhall Conference to pluck the 19-year-old striker Jason Roberts from Hayes for pounds 250,000. Roberts is the nephew of Cyrille Regis, the former England and West Bromwich Albion striker, who also began his career with Hayes.
"Roberts reminds me of Chris Armstrong. He obviously needs time to develop, but he is a very good prospect," Mark McGhee, the Wolves manager, said.
Notts County have escaped with a warning after an incident during last month's game against Lincoln City when the referee was allegedly assaulted by a spectator.
The Football Association has notified County that, after carrying out a full inquiry, it has decided not to take any further action.Reuse content