Redding first joined McLaren in 1995 as chief mechanic following a seven-year stint with Benetton. He briefly left the team for a three-year spell at Stewart Grand Prix but returned to Woking in 2000.
A McLaren spokesman confirmed Redding's departure to Motorsport.com.
"We can confirm David Redding is leaving McLaren Racing.
"He will be replaced by Paul James, who will become team manager, with a focus on the operational and managerial nature of the role.
"Our head of race operations Andrea Stella will assume some of the role's sporting responsibilities and engagement with the FIA. Kari Lammenranta will replace Paul as our new chief race mechanic."
One team's loss is another team's gain however, as Williams appears to be stepping up its recruitment efforts.
In addition to Redding, Williams has allegedly agreed terms with former Mercedes tech boss Paddy Lowe to join its ranks as a director and shareholder.
Lowe was placed on gardening leave last month by Mercedes but his move to Williams is expected to be completed very soon.