Swansea players Joe Allen and Darren Pratley have praised the team's work ethic following play-off glory.
Despite romping to a 3-0 first-half lead at Wembley, Brendan Rodgers' side came under severe pressure as Reading fought back to make it 3-2.
The Royals were denied the chance to move level after Andy Griffin bundled over Fabio Borini in the penalty area, allowing Scott Sinclair to convert the penalty and complete an impressive hat-trick to put the result beyond doubt.
After the final whistle, Allen admitted that the men in white had been thoroughly tested en route to victory.
"We showed brave resolve. Reading pushed us to the limit today but we just had enough on the day to pip them," he told Sky Sports.
"The focus of the half-time team talk was to carry on playing the way we always do. It's easy to get carried away at 3-0 but we had to keep going until the final whistle.
"It's been a massive journey for me and the club. Only a few years ago we were almost out of the Football League and here we are celebrating promotion to the Premier League."
Fellow midfielder Pratley, a second-half substitute, added: "When I left Fulham I said I wanted to get back to the Premier League. I said then I thought Swansea were the right club...and we've achieved it.
"There have been a few managers who have done well: Roberto (Martinez), Kenny (Jackett) and Paulo (Sousa) deserve credit but Brendan has taken us to another level. To get to the Premier League is a credit to everyone."