The France international completed his move to the Liberty Stadium on Friday, having become a free agent after turning down a new deal with Lyon.
Gomis was a regular scorer in Ligue 1, registering 10 goals or more in eight successive seasons, and Monk expects the 28-year-old to prosper in his new surroundings.
"I'm very happy. You are talking about a quality striker who has played international, Champions League and top-flight football in France for a big club," Monk told Swansea's official website.
"It's a fantastic signing; a very big and important signing for the club. It shows just how far we have come that we can attract a player of his quality.
"He's a player that can excite the crowd, make and score goals. He's always done that wherever he's been - and that's what we want him to keep doing here.
"We want him to be an important cog in the squad and help us to continue building.
"He asked a lot of questions about the squad and the strengths of the players. He wants to settle into the squad as quickly as possible and do well on the pitch. That is the type of player we want at this football club."
Gomis believes he can strike up a strong partnership with Wilfried Bony, the Ivory Coast forward who scored 26 goals in his debut campaign with Swansea last term.
"I do not see Wilfried Bony as competition, more of an association, because I know we can also play perfectly together,’’ added Gomis.
"We can benefit each other and that will be strong for the team."
