The news anchor - who took over the post from Katie Couric in 2006 - was first thought to be considering leaving the network earlier this month.
According to The Hollywood Reporter, Viera will quit the programme in June after ending her current contract three months early.
Newscreader Ann Curry will replace her, with correspondent Natalie Morales filling Curry's current position. An announcement on the new line-up is expected to come as early as next week.
Vieira's decision to exit the show is believed to be motivated by her desire to spend more time with her ailing husband, whose illness she has previously admitted that she feels "cheated" by.
Katie Couric recently confirmed speculation that she has decided to exit CBS Evening News after her current contract runs out in June. Her former NBC colleague Matt Lauer recently denied speculation that he would be leaving The Today Show.