Farrell is Europe's best
This honour was bestowed upon him after he guided Saracens to a second successive Champions Cup title at Murrayfield at the weekend.
England playmaker Farrell received the award from European Professional Club Rugby shortly after kicking 13 points as Saracens, also the reigning English champions, beat French side Clermont 28-17.
Munster coach Foley died suddenly in Paris in October aged 42 just hours before the Irish province were due to play their first European Champions Cup match of the season against Racing 92.
Former back row forward Foley was previously a mainstay of the side that helped Munster become a major force in the European game.
With the agreement of the Foley family and Munster, EPCR commissioned a trophy to honour his contribution to European rugby union.
The award winner was chosen by a combination of public vote and a panel of rugby experts, with Farrell emerging from a shortlist that included Saracens teammate Maro Itoje, last year's winner, Clermont's Camille Lopez, Garry Ringrose (Leinster) and Christiaan Stander (Munster).
"This is a fitting way to honour Anthony's memory," said EPCR chairman Simon Halliday in a statement.
"He was a great player and a great leader as well as a galvanising force in Munster's European odyssey."
Former England international Halliday added: "I would like to thank the Foley family and Munster Rugby for allowing us to create this trophy for now and for the future."
Foley made 86 European Cup appearances for Munster, played in three finals and captained the side to their first final victory in 2006. He remains the province's top try scorer in Europe with 23.
He also played 62 times for Ireland, captaining his country on three occasions, before moving into coaching and eventually taking over at Munster in 2014.
Past winners: Ronan O'Gara (Munster Rugby – best player of first 15 years of European club rugby tournaments); Sean O'Brien (Leinster Rugby) 2011; Rob Kearney (Leinster Rugby) 2012; Jonny Wilkinson (RC Toulon) 2013; Steffon Armitage (RC Toulon) 2014; Nick Abendanon (ASM Clermont Auvergne) 2015, Maro Itoje (Saracens) 2016.
