The 19-year-old had a month left to run on his existing Emirates deal and chose not to extend his stay due to the lack of first-team opportunities. Willock only managed two appearances for the Arsenal first-team last season, these coming in the EFL cup as a substitute.
Reports suggest the young striker has put pen to paper on a five-year deal with Benfica.
Arsene Wenger rated Willock highly and were hoping to tie him down to a new long-term deal, but the teenager, who has been with Arsenal since 2003, opted to prove himself elsewhere.
Everton, Manchester City, Celtic and Borussia Dortmund were all thought to be keen on signing him as well.