France international Gomis joined Swansea from Lyon at the start of the season, but has had to play a bit-part role behind in-form striker Wilfried Bony.
Gomis has made just three Premier League starts, scoring once, and Monk further added to his forward options on Tuesday by recruiting Oliveira, who will join on loan from Benfica in January for the remainder of the season.
The arrival of Oliveira will further boost Swansea, with Ivory Coast international Bony set for a period of absence when he travels to the Africa Cup of Nations in mid-January.
"I am happy to have completed the deal for Nelson," Monk told a media conference ahead of Friday's clash with Aston Villa.
"I said before that we needed to look at the position, because we need another player to push Bafe [Gomis] when Wilfried Bony is away.
"And Nelson is a very good player. I have watched him a lot, especially since the start of the season, because his name came up in the summer and we have been looking at him throughout that period."
When asked if Oliveira's arrival could mean that Gomis' days at the Liberty Stadium are numbered, Monk denied that was the case.
"Bafe is a Swansea City player," he added. "I have really enjoyed working with him. He is a great professional, a good guy and a top, top player.
"I am trying to give him that game-time, but it has been difficult with Wilfried playing so well.
"It can be frustrating for players, but Bafe has been brilliant and we're now coming into a period where he'll be playing and the shirt will be his to lose.
"I can't stop the speculation, but Bafe is a Swansea City player."
