AUTOSPORT reported on Thursday that Morris has handed in his notice at his current outfit, and he will officially relinquish his role on Monday.
Morris will be switching to McLaren when he is released from his contract at Sauber, and will work under its technical director Tim Goss.
A McLaren spokesperson said: "Matt Morris will join McLaren Racing as engineering director once his current contractual situation with Sauber is resolved.
"Matt will work for our technical director, Tim Goss, to ensure our engineering standards and technical decision-making capabilities are of the highest quality.
"During a period of intense technical challenge within Formula 1, Matt's appointment is the first step in an ongoing programme to strengthen the engineering department as our organisation prepares for the arrival of Honda in 2015."