Curtis has been in caretaker charge since Swansea sacked Garry Monk on December 9 after a run of only one win in 12 games.
Under Curtis’ command, Swansea have won one, drawn two, and lost two, and are currently two points above the Premier League relegation zone.
Announcing the appointment on the club’s official website, chairman Huw Jenkins said: “Alan Curtis and the current staff setup will continue until the end of the season. We firmly believe it is the right decision for Swansea City.”
It is understood that former boss Brendan Rodgers was Swansea’s preferred choice to succeed Monk.
But Rodgers wanted to take an extended break after leaving Liverpool in October. Jenkins’ search for a manager took him to South America, where he met former Argentina, Chile, and Athletic Bilbao coach Marcelo Bielsa.
Those discussions floundered and Gus Poyet, Roberto di Matteo, and Jose Mourinho’s former Chelsea assistant Jose Morais were all strongly linked with the position as Curtis oversaw an improvement in performances.
Swansea beat West Brom and drew with West Ham and Crystal Palace, with the two defeats being narrow 2-1 losses at Manchester City and Manchester United.
“Alan has been with us through good and bad times and was part of the management team that helped the club secure its Football League status over 12 years ago,” Jenkins said.
“He is fully aware of the next important job he has ahead of him to dig deep and find the required levels of performance and motivation to secure our Premier League status — our main goal this season.
“We believe there is nobody with more knowledge and experience of the club to do that than Alan Curtis.
“He has served Swansea City so well for more than 40 years and played an integral part in our recent success under the likes of Roberto Martinez, Paulo Sousa, Brendan Rodgers, Michael Laudrup, and Garry Monk.
“We have a person at the helm who fully represents all Swansea City stands for, has the respect of the players, and who will provide the calm reassurance and encouragement of our footballing beliefs.
“We have all been impressed with the way he has improved performance levels over the last five games.
“The players have obviously responded to him because we have seen an uplift in performances.
“I know some people will query why we didn’t have a replacement lined up when we parted company with Garry Monk, but we didn’t expect to be in the situation we were in when you look at our position mid-September. We hoped and expected things would eventually turn around. When they didn’t, we felt we had to act quickly in the best interests of the club going forward.”