Templeton, who has also turned out for Hearts and Raith Rovers, was available on a free transfer after enjoying an impressive campaign with Hamilton last term. He has penned a two-year deal with Albion after revealing he was keen to try his luck in England.
Templeton said: “I have always wanted to come down south and test myself down here and I think the club is perfect for me.
“The way the gaffer wants to play football will suit the way I play.
“I didn’t want to go my whole career in Scotland without trying it in England.”
Fraser made 106 appearances for United after making his first-team debut against Celtic in May 2014, but departed last month following their failure to win promotion to the top-flight.
Hearts boss Craig Levein was known to be a huge admirer of the player, however he has also opted to test himself south of the border and last night agreed a contract until the summer of 2020.
Fraser said: “I was coming to the end of my contract [at United] and was speaking about a new one, but I just felt a change was needed – to move away, grow up and try and improve as a player. Everything about this move felt right.
“I think it’s the right move for me. When I found out what clubs might be interested, this was the best feel I got.
“Having spoken to the manager [Nigel Clough] and coming down to see the ground and training facilities I think it’s a club where I can get better as a player.”
Templeton and Fraser follow ex-Ross County duo Liam Boyce and Jackson Irvine in making the switch from the SPFL to the Pirelli Stadium.
Brewers manager Clough added: “The Scottish market remains a good option for us as we look to build a team for League One.”