The leader of Swansea Council has described the Swans' recent years as 'a footballing fairytale'.
The council has confirmed a victory parade for the Swans will take place on Tuesday.
– Swansea Council Leader David Phillips
The eyes of the sporting world were on Wembley and it's our club which will be the toast of football. I want to pay tribute to Michael Laudrup, his playing staff and the backroom staff for this magnificent achievement.
The Swans fans were fantastic and built on their growing reputation as some of the most loyal and passionate supporters in the country. They can now look forward to a European adventure that not so long ago would have been little more than a dream.
Swansea manager Michael Laudrup has spoken of his pride after seeing his side thrash Bradford 5-0 to win the Capital One Cup at Wembley.
Laudrup told Sky Sports 1: "I'm very proud of my team today. I think it was a great performance."
He also hailed the triumph as the best of his managerial career.
– Michael Laudrup
As a manager it's absolutely at the top, winning a trophy for the first time in 100 years.
The first trophy is always special, and now next year in Europe... it's a nice experience.
Swansea City have made history - winning the Capital One Cup after beating Bradford 5-0 at Wembley.
Goals by Nathan Dyer and Michu have put Swansea City in a magnificent position as the two sides enter half-time.
Swansea City kick off against Bradford City in the final of the Capital One Cup at Wembley at 4pm.
It is Swansea's first major cup final in the club's 100-year history, and they are 90 minutes - plus extra time and penalties if required - away from winning their first major cup, and qualifying for European football next season.
League Two side Bradford also have history on their minds. They have knocked out three Premier League teams already, and become the first team from the fourth tier to play in a major Wembley final.
The ITV Sport website has live updates on the action.