The 19-year-old follows Wayne Rooney, Raheem Sterling, Lionel Messi and Sergio Aguero in winning the award for Europe's best player aged under 21.
Rashford and Sanches' club team-mate Kingsley Coman also made the podium.
Portugal international Sanches will receive the award at a ceremony in Monte Carlo on Monday.
The prize, voted for by journalists across Europe, was established by Italian newspaper Tuttosport in 2003, who revealed this year's winner on their front page.
Sanches has played eight games for the German champions this season, having joined in the summer for £27.5m, and has 11 caps for Portugal.
At Euro 2016 - then aged 18 - he became the youngest player to feature in a European Championship-winning side and won the Young Player of the Tournament award.
Bayern Munich midfielder Renato Sanches has won the European Golden Boy award, beating Manchester United and England striker Marcus Rashford.