The agreement, believed to be a four-year contract, will replace the club's existing deal with Vodafone, which expires at the end of this season.
The announcement brings to a close six months of media speculation with a variety of global brands linked to the sponsorship. The most recent of these was gambling firm Mansion, which accused the club of "double dealing" last week after negotiations for the contract stalled.
Mansion stated that it had believed itself to be in an exclusive negotiation period with the club. Manchester United however maintained that it had never stated in any meetings with the gambling firm that it was not talking to other potential sponsors.
The football club had also been in talks with two Middle Eastern airlines, Etihad Airways and Qatar Airways, prior to talks with Mansion. The two airlines were then again connected to the club after talks with Mansion ended over the weekend.
Unusually for a Manchester United shirt sponsor, AIG is not renowned as a consumer-facing business. It predominantly operates in the business-to-business area, although it does have some consumer-facing operations.
The insurance giant was also pivotal in backing Malcolm Glazer's takeover of Manchester United last summer.
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