Rangel handed Swansea captaincy
Britton relinquished the armband to take up the role vacated by Claude Makelele last week, although he forms part of Clement's backroom team as a player-assistant coach.
Clement had no doubts about giving the captaincy to Rangel, who is in his 11th season at the Liberty Stadium having arrived in 2007 from Catalan side Terrassa.
The 35-year-old right-back admits the news came as a shock to him after he'd made just one appearance in the Premier League this term.
"I never thought I would end up as a captain, but I am proud and honoured and full of enthusiasm after being given this chance," he told the club's official website.
"I thanked the manager. He could have chosen someone who would play a bit more regularly than me, but it is not just on the pitch that you need some leadership and I am happy to take this job.
"I had a lot of dreams to achieve when I first came here, one of them was to become a Premier League player, which I achieved.
"I've got Swansea in my heart. I love the club and the most important thing is that we stay in the Premier League this year."
Clement added: "Given his age, experience and the excellent service he has given to this club over a number of years, Angel is the right choice to be club captain.
"He is a great role model and a very good professional who all other players can look up to."