Guidolin, 60, was appointed in January on a six-month contract after Alan Curtis’ temporary spell in charge, with the club in the relegation zone.
The Italian has led them to 11th place – 12 points clear of the bottom three, and they could finish in the top half.
“The players really like him so it’s a popular decision,” said Britton.
“The manager came in a difficult period, couldn’t speak the language [and] he is new to the league.
“But he’s come in, settled very well and he’s picked up the language well and got to know the squad.
“He’s done very well, 24 points in 15 games… You can’t argue with that.
“We’re delighted for him, he’s a good guy.”
Swansea – who host Manchester City in their final Premier League game of the season on Sunday – have won seven and drawn three of Guidolin’s 15 games in charge so far.
The Welsh side, currently 11th, could leapfrog Stoke into 10th place if the Swans win and Mark Hughes’ team fail to beat West Ham.
Britton says Swansea’s upturn in fortune since January has been especially significant given the lucrative television deal which begins in time for the 2016-17 season, which will see top-flight clubs share more than £5bn.
“We could end up with a decent position in the league which wouldn’t look too bad, but I think at the same time we have to remember that some of the performances haven’t been great along the way,” said Britton.
“Another season in the Premier League, we all knew what it meant this season to stay in the league.
“Everyone knows the amount of money that is coming into the clubs who stay there, so it’s a big one for us.”
Midfielder Gylfi Sigurdsson was named supporters’ player of the year at Swansea’s end-of-season awards, while Modou Barrow won young player of the year and Curtis was honoured with a lifetime achievement award.
Sigurdsson has scored 11 goals this season, a contribution which has been crucial to the Swans’ rise up the table.
“Gylfi has been outstanding, especially in the last three months when we needed the players to really stand up and be counted,” said Britton.
“He’s scored a lot of vital goals that won us points, also assisting goals as well.
“He fully deserves the award. I think he has been fantastic for us this year in a difficult period.
“A great professional, a good guy to have around the club and obviously the main target, like all the time we get player of the years, is to hold on to them in the summer.”