Damsgaard joined the Genoa-based club two years ago, making 49 appearances and registering two goals and four assists in all competitions. He missed a large part of last season through injury.
"Mikkel is, in my opinion, another classic Brentford signing. He is a young player with big potential to develop further," manager Thomas Frank said.
Brentford host Manchester United on Saturday in their second Premier League match of the season after a 2-2 draw at Leicester City last week.