Emnes spent two loan spells at Swansea before joining from Middlesbrough for an undisclosed fee on Wednesday.
And Monk feels the 26-year-old can play a major role next season as Swansea look to improve on a disappointing Premier League campaign.
"Marvin's an important signing for us," Monk told The South Wales Evening Post.
"I think he has really contributed in the spells he has been with the club.
"He was one who we always wanted to bring in, so thankfully Marvin has agreed to come.
"He will fit well into a squad he already knows, and he has proven at this level that he can contribute.
"I think he feels at home here. He's been made to feel welcome during his time here before, and he knows what the club means to the fans and also the players."
Swansea have already signed forward Bafetimbi Gomis, goalkeeper Lukasz Fabianski and defender Stephen Kingsley in the close-season and Monk expects more arrivals before the Welsh club open their top-flight campaign at Manchester United in August.
"Hopefully we'll have one or two more bits and pieces of business that can be done, but as in terms of building the squad, I am very happy," he added.
