Former Sheffield Wednesday boss Carvalhal was axed from Hillsborough on Christmas Eve but has since held successful talks with Swansea.
Carvalhal, 52, even watched Swansea's game at Liverpool on Boxing Day from the directors' box and is in pole position to take charge.
The Portuguese had two and a half years at Hillsborough, his style of football suits Swansea and his experience in the Championship also gives him an advantage if they cannot beat the drop.
Swans chairman Huw Jenkins said: “We are very pleased with the appointment.
“We felt we needed to get the managerial situation resolved as soon as possible and while the timing is not always perfect, we can look forward to the second half of the campaign with renewed optimism.
“Carlos' time at Sheffield Wednesday, which included securing two consecutive play-off places, highlighted that he has great character and personality to lead the squad and the football club, which is vital at such a crucial time.
“He has built up a lot of experience over the years which will ensure the team is structured and organised.
“He is driven and ambitious and while he has a big challenge ahead of him, I know he will tackle it without fear."