McElwee, who joins the agency on 22 March, replaces Victoria Davies, who is joining TBWA\London as the head of account management.
At Euro RSCG, McElwee was responsible for Peugeot, the Greater London Authority and Solve-It. He joined the Euro RSCG Peugeot team in 1999 from Lowe Howard-Spink and became the head of client services in July 2001. He was made the joint head of account management last summer, following the creation of Euro RSCG London.
The move reunites him with former colleagues such as the M&C managing director, Tim Duffy, with whom he worked at Saatchi & Saatchi, before the founding of M&C Saatchi.
Duffy said: "McElwee has tremendous energy and talent. We were impressed by his strategic flair and instinct for creativity."
Davies joins TBWA in April and will join the agency's managing partner group.
TBWA's chief operating officer, Matt Shepherd-Smith, said Davies' hiring was part of an initiative to strengthen the agency's account management. The role was previously held by Shepherd-Smith, but has been vacant for more than two years.