However some writers questioned his suitability for the prize.
The 75-year-old did not mention his Nobel Prize during a concert at the Las Vegas Cosmopolitan hotel on Thursday.
Writing on Facebook, Baez said: "The Nobel Prize for Literature is yet another step towards immortality for Bob Dylan.
"The rebellious, reclusive, unpredictable artist/composer is exactly where the Nobel Prize for Literature needs to be.
"His gift with words is unsurpassable. Out of my repertoire spanning 60 years, no songs have been more moving and worthy in their depth, darkness, fury, mystery, beauty and humour than Bob's.
"None has been more of a pleasure to sing. None will come again."
Baez championed Dylan as he was making his name in the early 1960s and covered a number of his songs, as well as being romantically involved with him.
Other figures to praise the Nobel panel's decision included US President Barack Obama, who wrote on Twitter: "Congratulations to one of my favourite poets, Bob Dylan, on a well-deserved Nobel."
Bruce Springsteen also congratulated Dylan by posting a passage from his autobiography on his website. In it, he described Dylan as "the father of my country".
"Highway 61 Revisited and Bringing It All Back Home were not only great records, but they were the first time I can remember being exposed to a truthful vision of the place I lived," he wrote.
Dire Straits' Mark Knopfler wrote on Facebook he was "delighted" for Dylan. He explained: "Bob Dylan has been a great songwriter since he was a teenager and nothing has stopped him in continuing to write and bring his gifts to the world."
Author Philip Pullman said on Twitter that Dylan was "a great choice for the Nobel Prize".
He added: "One result might be to open the prize to genre fiction as well as the 'literary' sort."
Writer Sir Salman Rushdie also praised Dylan's win, saying: "From Orpheus to Faiz, song and poetry have been closely linked. Dylan is the brilliant inheritor of the bardic tradition. Great choice."
But Trainspotting author Irvine Welsh voiced his displeasure on Twitter, saying: "I'm a Dylan fan, but this is an ill conceived nostalgia award wrenched from the rancid prostates of senile, gibbering hippies."
Fellow novelist Hari Kunzru said the prize could have been better used to draw attention to lesser-known authors and publishers.
He wrote: "People could have been introduced to Marias or Ngugi or Yan Lianke or Solstad or Ugresic instead of confirming their Dylan love. So, meh."
US author Jodi Picoult also conveyed ambivalence, accompanying a message saying she was "happy" for Dylan with the Twitter hashtag "#ButDoesThisMeanICanWinAGrammy?"
Sara Danius, permanent secretary of the Swedish Academy, said Dylan was chosen because he was "a great poet in the English speaking tradition".