The 52-year-old, appointed as Paul Clement's successor in December, was unable to stop the Swans' descent to the Championship during his five months at the Liberty Stadium helm.
Swansea, now seeking a fifth permanent manager in two years, were officially demoted to the second tier with last Sunday's 2-1 loss to Stoke City.
Speaking after that match, Carvalhal suggested that the club's owners wanted him to stay on for another season, but he refused to confirm whether he would step aside.
Five days on from the final-day home defeat to Stoke, Swansea have confirmed a parting of ways.
In a statement on the club's official website, chairman Huw Jenkins said: "We'd like to put on record our thanks to Carlos for his enthusiasm, hard work and commitment since arriving at the club in December.
"Naturally, we are all disappointed with the club's relegation from the Premier League, and following discussions with Carlos, we felt it was in the best interests of both parties that we move in a new direction.
"We will now be looking to appoint a new manager in readiness for the 2018-19 season. While there are already rumours linking us with several managers, it is vital that we identify the right person to take this team forward."
City, who failed to win any of their last nine league matches, have also announced the departures of first-team coaches Joao Mario and Bruno Lage, along with match analysts Jhony Conceicao and Paulo Sampaio.