Grant, who played 75 times for the Canaries towards the end of a career that included over 400 games for Scottish giants Celtic, will take over on Monday once compensation has been agreed with the Hammers.
The Scot, who has been Alan Pardew's number two since 2004 and helped them back into the Premiership, was one of a number of former Norwich players linked to the job. It is believed Ian Crook was interviewed, and Mark Bowen was the favourite for the most part.
It is Grant, however, who will take over the reigns from Martin Hunter in his first managerial job. Discussions between the City board and their West Ham counterparts should be convivial given the amount of business conducted between the sides in recent months. Dean Ashton and Robert Green have moved in the opposite direction to the new Norwich boss, who is expected to be at Loftus Road tomorrow to watch the side play QPR.