The Upton Park club have confirmed the appointment and will parade the former Watford and Gillingham boss at a news conference on Thursday.
Roeder - whom Glenn Hoddle had hoped to tempt to Spurs - will graduate from his job as a coach at Upton Park to end the Hammers' five-week search for a new boss.
He has been on the staff for two years, and only emerged as a late contender for the top job at West Ham.
"When Harry Redknapp brought me in to join the coaching staff I never dreamed that I would be his successor," Roeder told the club's official website.
"Being a local lad, I always followed the Hammers and hoped that one day I would be involved with the club.
"I know many supporters expected a bigger name to take over and I realise the huge responsibility that goes with the job, but I am ready to embrace the task ahead.
"This is a very proud day for me."
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Managing director Paul Aldridge added: "We are delighted to give one of the game's most respected young coaches the opportunity to take the team forward.
"We were very impressed with the ideas Glenn put forward.
"There will be substantial money made available for Glenn to spend on new players.
"We also plan to announce important additional changes to the managerial and coaching staff shortly."
Roeder's appointment comes after West Ham's failed attempts to lure a succession of top-flight managers.
Once a row over transfer funds ended with Redknapp's departure, Steve McClaren turned the job down, while Alan Curbishley, David Moyes and Alex McLeish were also linked with the vacancy.
However, Roeder's appointment has already been welcomed by Hammers youngster Joe Cole.
He said: "When people ask me about Glenn Roeder, I will always say he is probably in the top three coaches I have ever worked with," Cole told the club's official website.
"I know being a manager is a lot different, but if there is anyone who I know personally that can do the job - he can.
"He really has got all the credentials; the lads love him, he knows how to coach and he knows his football more than anyone.
"Everyone needs a chance in life, don't they?
"I know all the fans will get behind him and we will look to have a good season."
Roeder was in charge of Watford between 1993 and 1996. He left the club when they were bottom of the First Division.
He also lost 22 of 35 games in charge of Gillingham between August 1992 and July 1993.