City captain Kompany missed the 2-2 draw with QPR before the international break with a calf strain, and did not feature for Belgium in their outings against Iceland and Wales.
But manager Manuel Pellegrini announced in his press conference on Friday that the influential central defender has recovered and is fit for the match at the Etihad Stadium.
"Vincent Kompany had a small problem but he is available for the game tomorrow," he said.
Lampard, who had been a slight doubt despite appearing as a second-half substitute against QPR, is also in the frame, Pellegrini confirmed, although David Silva (knee), Edin Dzeko and Aleksandar Kolarov (both calf) are out.
City have faltered in recent weeks, winning just once in their last six matches in all competitions, and Pellegrini hopes Saturday's match will mark the start of an improved run of form.
"I hope we can return to our normal form now the international break is over," he added.
"Swansea are a very good technical side and we are expecting a difficult afternoon."
Yaya Toure - whose performances have attracted criticism this season - helped Ivory Coast qualify for next year's Africa Cup of Nations during the international break, meaning City will have to cope without the powerhouse midfielder when the tournament takes place in January and February.
"It was very important for Yaya to qualify for the Africa Cup of Nations and I am very happy for him," Pellegrini said.
"Of course we will miss Yaya in January but we will decide how we cover his absence in December."
