Radford has previously been in charge of the High Performance Centre (HPC) in Barbados and will now work with the senior team, which is coached by Ottis Gibson, on a tour-by-tour basis beginning with the home series against Australia which starts this month.
After a brief playing career which amounted to 14 first-class matches, Radford was made Middlesex coach in 2007 before moving to the Caribbean in 2010.
Williams, the former West Indies wicketkeeper who played 11 Tests and 36 one-day internationals between 1992 and 1998, said he still hoped play a role in the future of Caribbean cricket.
"I am disappointed, but these things happen in life and you have to pick up the slack and move on," Williams told the Trinidad and Tobago Express. "Just a couple of days ago they called me about the position. They wanted a coach to work with the younger batters.
"I enjoyed my time. It was really a great experience and I want to thank the West Indies Cricket Board for that experience. It is not the end of the road. I hope the West Indies Cricket Board knows that I still have a lot to offer West Indies cricket."
Edited by Andrew McGlashan