Swansea's 2-0 win at Sunderland on Saturday left fellow strugglers Hull City needing a result away to Crystal Palace this afternoon, but the Tigers were on the end of a 4-0 thrashing which condemned them to an immediate return to the Championship.
Clement was sure that the battle to avoid the drop would go to the final day of the season, but is relieved to have sealed a seventh consecutive season in the top flight with one game to spare.
"I am very proud of what we have achieved in the second half of the season. Especially when you put into context where we were when I arrived - bottom of the table with just 12 points from 19 games. It's been a collective effort from everyone connected to the club; so congratulations to the players, backroom staff, club staff and definitely our supporters for their help in getting us over the line," he told the club's official website.
"I honestly thought it would go down to the last game of the season. But credit to the players for showing the form they have over the last four games to pick up 10 points from a possible 12. They deserve to be where they are - playing in the Premier League again.
"I'm not complaining it hasn't gone to the last game as I predicted. And I'm sure the fans will feel the same way after everything they've been through this season. Our supporters have been amazing. It's been tough for them at times, but they've stuck with us all the way and I'm delighted for them more than anyone.
"I'm looking forward to enjoying the last game of the season with them at the Liberty on Sunday. It should be a fantastic atmosphere. We will be aiming to finish the season strongly and reach 41 points. Then we can look forward and make sure we are stronger next season."
Swansea will finish their season at home to West Bromwich Albion next Sunday.