Bayern Munich play host to Real Madrid on Tuesday before Chelsea face Atletico Madrid at Stamford Bridge on Wednesday.
And UEFA.com announced: "A short announcement will be made in the teams' native languages explaining the silence while a montage of the two coaches, who both died in recent days, will be displayed in the stadiums.
"Teams have been given the option of wearing black armbands."
After a lengthy playing career, Vilanova worked as an assistant to Pep Guardiola at Barcelona during a gloriously successful period for the club.
After Guardiola stepped down, Vilanova took charge and led Barca to the 2012/13 La Liga title but he had to resign in July last year and sadly died at the age of just 45 on Friday after a battle with throat cancer.
And Serbian coach Boskov passed away at the age of 82 on Sunday.
He won a domestic double with Real Madrid in 1979/80, guided Sampdoria to their only Serie A title in 1990/91, and took Yugoslavia to the quarter-finals of Euro 2000.