Noonan's hiring comes seven months after longtime coach Trevor Adair resigned following his arrest on charges of attacking his teenage daughters.
Clemson assistant coach Phil Hindson stepped in after Adair's resignation in June. The Tigers went 6-12-1 under Hindson.
The announcement was made Monday afternoon by Clemson Athletic Director Terry Don Phillips.
Noonan becomes only the program's fifth coach in the 75-year history of Clemson soccer. The Tigers won NCAA championships in 1984 and 1987 under the late I.M. Ibrahim and has won 13 Atlantic Coast Conference Championships.
"Clemson has a lot of history and success in collegiate soccer and we look forward to adding on to that success in the future," said Noonan. "My family and I are excited about coming to Clemson and joining the Tiger family. To leave a place like Brown, it had to be a special opportunity, and Clemson was this special opportunity."
Clemson is considered one of the nation's top men's programs with strong support from the school administration and considerable fan interest,
In 2009, Brown finished with an 11-3-5 record overall and advanced to the NCAA Tournament's second round. Noonan guided the Bears to the Elite Eight of the NCAA Tournament in 1995 and 2000.
Noonan has a 160-77-31 record in 15 years at Brown. He has a 224-116-1 overall mark in his 21 seasons as a collegiate head coach. He also coached at Wheaton College and the University of New Hampshire.