The pair will front their own shows during the festive period on the radio station later this month.
Former Only Way Is Essex star Wright will host special editions of Party Classics on Christmas Eve and Christmas Day from 7pm.
He will then take on a permanent position as the host of the Friday and Saturday evening Club Classics show on the station at 7-9pm.
He said: "I've always listened to Heart from being a kid on the way to school and now getting ready for a night out, so to be presenting my own radio show on the station is a great honour.
"I had to pinch myself when I found out and I can't wait for my first show."
Klass will host her own special Myleene's Klass Christmas on Christmas Eve from noon.
X Factor act Ella Henderson will perform during the show alongside other musical guests.
She said: "I'm so excited to be joining the Heart presenter line-up.
"To be given my own show, a piano and the chance to work with some incredible people (as well as the seemingly constant supply of mince pies) is a lovely way to get in the Christmas spirit."
Global Radio's Director of Broadcasting Richard Park added: "We are thrilled with the new faces joining Heart this Christmas and New Year. What a great way to end a successful year and kick start 2013!"
Mark Wright is also expected to return to The Only Way is Essex during tomorrow night's episode (Wednesday, December 19).