In addition, Mark Fairbanks and Tim Riley, previously creative directors at AMV, have been promoted to creative partners to bolster the agency's senior creative partner line-up, which includes Steve Jones, Martin Loraine and Thiago de Moraes.
Rossi and Grieve worked at Glue Isobar for a year and, before that, were creative directors at Bartle Bogle Hegarty for 14 years, where they created the award-winning Barnardo's "heroin baby" work.
They also produced work including Lynx "billions", Audi "fish" and the "lost lives" campaign for St John Ambulance. Their awards tally includes two Cannes gold Lions, three D&AD Pencils, and a Campaign Big Awards gold.
Fairbanks and Riley have been promoted after long spells at the agency. Riley has worked at AMV for 15 years and won awards for his work on The Economist, Mercedes-Benz, BBC Two and Birds Eye. Fairbanks, who has been at the agency for eight years, has worked on The Economist, Doritos and Guinness.
Rossi and Grieve, in common with the other creative partners, will report to AMV's executive creative director, Paul Brazier.
Brazier said: "I am excited about Alex and Adrian joining us and, along with Mark, Tim and the other creative partners, I really feel AMV is moving forward with the best creative talent available."