Winkleman replaces Bruce Forsyth and joins Tess Daly on the Saturday night, multi-award winning reality show.
The presenter said that she was "honoured" and "thrilled" to be given the job.
Forsyth stepped down from the show after 11 series earlier this year. He will return for Christmas and Children in Need specials, but Winkleman and Daly will host the main series throughout the autumn.
"I have loved Strictly since the second it appeared on our screens and I am honoured and thrilled to now be part of the Saturday night team," said Winkleman.
"Working alongside Tess is always fantastic and I can't wait to spend the weekends with her, our amazing dancers and the greatest judging panel on the planet. Sir Bruce is a living legend and we'll all miss him very much."
Winkleman previously hosted Strictly spin-off show It Takes Two for six years and more recently presented the Sunday night results shows to give Forsyth a rest.
She has also filled in on the Saturday night shows before when Forsyth has been absent with illness or planned breaks.
Why Claudia Winkleman has to replace Bruce Forsyth
Tess Daly described Winkleman as part of the Strictly family and said that she was excited to be hosting the show with another woman.
"It's really exciting having two women host the show, and we are great mates so there'll be lots of fun to be had on and off the dancefloor, and of course I'll look forward to being reunited with Brucie for the Children in Need and Christmas shows," said Daly.
BBC One controller Charlotte Moore said: "Tess and Claudia are a fantastic duo and natural successors to Strictly's presenting lineup now that Sir Bruce has decided to step down. Their commitment and passion for the show make them the perfect pairing to take Strictly into a new era."
Winkleman was Digital Spy readers' No.1 choice to take over from Forsyth, collecting over 31% of the votes.
Strictly Come Dancing returns to BBC One in the autumn.
Early celebrity lineup rumours for 2014 include Coronation Street's Michelle Keegan, soap star Michelle Collins, X Factor winner Joe McElderry, Jayne Torvill and Christopher Dean, and Andy Murray's mum Judy.