From November 6, Blackburn will start presenting the chart rundown, which airs on Radio 2 every Sunday between 1pm and 3pm.
Pick Of The Pops, which is based on the Top 20 UK singles chart, became popular on Radio 1 in the late 1960s, but the show's last edition in its original form was aired in 1972.
The programme was resurrected on Radio 2 in 1997 hosted by Alan Freeman, before Winton took over in 2000. Winton's final edition of Pick Of The Pops will be broadcast on October 30.
"I'm delighted to be taking up the reins of one of radio's most iconic and famous shows at the UK's most listened to radio station," said Blackburn.
"I'm very much looking forward to indulging in two hours of fantastic, rarely heard music from across the decades each week."
Radio 2 head of programmes Lewis Carnie added: "I'm delighted to welcome Tony Blackburn to Radio 2 on a permanent basis. He is one of this country's legendary broadcasters and brings a wealth of knowledge of popular music spanning the years.
"I'd like to thank Dale for being such a tremendous host of Pick Of The Pops for the last decade, and I look forward to continuing our relationship with him on future Radio 2 projects."
Blackburn, who helped launch Radio 1 in 1967, recently presented the UK's Million Sellers Chart on Radio 2 over the August Bank Holiday weekend. He also presents The Best Of Soul & Motown show on BBC London 94.9FM every Sunday.