Craig Morgan and Ben Pringle have rejected new contracts at Rotherham and will leave the club on free transfers.
Saido Berahino can leave West Brom "if the deal is right", says manager Tony Pulis.
The 21-year-old had over a year left to run on his existing deal but the club were keen to tie him to a longer-term agreement.
Alfei, who has spent most of the season on loan at Wrexham, said: "I'm absolutely delighted. It's good to know the club has faith in me and there is nowhere I would rather be than Swansea."