Lampard was announced as the Rams' coach on Thursday, marking the 39-year-old's first job in management.
Redknapp, who is the uncle of Lampard and coached him at West Ham United, has backed the former Chelsea midfielder to impress at the Championship club.
"I spoke to Mel Morris (Derby chairman) when the position became available; I rang him up and had a chat with him, and things moved from there," Redknapp told reporters.
"He met Frank and I think it's a fantastic signing for Derby. We're talking about people going into management, Graeme Souness... Kenny Dalglish when he went in to Liverpool... So many lads have gone in and taken those jobs on, and if you understand the game... Frank hasn't spent the last 20 years with his eyes closed - he's an intelligent guy. He was the best professional and the best trainer I ever came across, by a million miles. He's going to take that now into management. The most important thing he needs is good players.
"Frank's been going into Chelsea and working with Jody with the younger players on a regular basis, getting his coaching badges and making sure he was prepared should a job come along. Obviously he's seen how good Jody [Morris] was at his job, and feels he is the ideal man to take with him. He knows him - I think they are good pals - and he trusts him, so it's a great chance for the pair of them; for Jody to move on from kids to working with senior players, and for Frank to take his first step into management."
Lampard will take over from the recently-departed Gary Rowett, who has agreed a deal with Stoke City to become their new manager.