Welch will work alongside Pierre de Bruyn, who was recently confirmed as the club's new head coach, replacing Andrew McDonald who is returning to Australia.
After a long career in the county game as an allrounder with Warwickshire and Derbyshire, Welch had spells as bowling coach at Essex and Warwickshire before becoming the head coach at Derbyshire ahead of the 2014 season. He quit that post in June of this year after what is believed to have been a disagreement over interference into team selection from outside the dressing room.
He has a particularly strong reputation as a bowling coach and worked with England Lions ahead of their series against Pakistan A in Dubai at the start of the year.
"Graeme will be a fantastic assistant for Pierre with his tremendous experience of county cricket as both a player and coach," Wasim Khan, the Leicestershire chief executive, said.
Leicestershire have also announced the signings of batsman Harry Dearden and seamer Gavin Griffiths, both of whom emerged through the Lancashire system, and seam-bowling allrounder Will Fazakerley, who graduates from the club's academy having previously impressed with Guernsey and in the Sussex youth system. Cameron Delport has also been re-signed for the 2017 white ball season.