Speaking on his Radio 2 breakfast show earlier, he said he had texted Jeremy Clarkson, Richard Hammond and James May before the announcement was made.
Hammond, he said, had wished him good luck and gave assurances he "didn't blame him" for taking the job.
Evans also said there will "absolutely" be a woman in the new Top Gear line-up.
But he said he would not have a female co-presenter just "for the sake of it".
"I want to have people who are extremely knowledgeable about cars... people who have great energy, good timing... who are keen to do things differently," he told Radio 5 live.
The BBC has yet to confirm the rest of the Top Gear line-up - but Formula 1 presenter Suzi Perry featured prominently in the audience of Evans' TV show TFI Friday last week.
In his first remarks about the Top Gear job, broadcast on Radio 2 at 08:15 BST, Evans said Clarkson had also wished him "the best of luck".
Clarkson "then gave me a piece of advice which I'm not going to repeat on the radio", the broadcaster told his listeners.
Clarkson's contract was not renewed by the BBC after he punched a Top Gear producer in March.
Evans, a noted car enthusiast, had previously ruled himself out of becoming taking over the show.
Evans said he had wanted Top Gear to carry on with Hammond and May and had not wanted to "contaminate the situation" by throwing his hat in the ring.
"Whenever I said 'I categorically rule myself out of running for office', it was because I didn't want to be a pawn in a chess game involving three of my friends."
The situation changed this week, he explained, with Hammond and May confirming they would not continue on the programme in Clarkson's absence.
This led to a conversation with Mark Linsey, the BBC's controller of entertainment commissioning, and an offer he felt he had to accept.
Top Gear, said Evans, was "the biggest television show in the world" and his "favourite television show of all time".
"I love producing TV... and so I said yes," continued the former TFI Friday host, who will lead an as yet unconfirmed line-up of new presenters.
Hammond, Evans went on, had told him he was "designed and built" for the Top Gear job and that his hiring was "always the BBC's very best option".
Evans also hinted obliquely that James May may play some role on the programme in future.
"We're going to meet up today and tomorrow and talk about things and who knows what might happen there."
Evans has signed a three-year deal to host and produce the BBC Two show, one of the corporation's most popular international exports.
It is watched by 350 million viewers worldwide, with overseas sales worth an estimated Â£50m a year.
Evans has also received the backing of Chris Goffey, who co-hosted Top Gear in the 1980s and 1990s.
The broadcaster, Goffey told BBC Breakfast, was "the obvious choice", asking: "Who else in TV is really clued-up about the cars and has got a persona to match Jeremy's?"
Speaking to Radio 5 live on Wednesday, Evans said he had started formulating ideas for the show on Saturday, adding they involved "evolution, not revolution".
"The films have got to stay there," he said of the elaborate film sequences that were a feature of the Clarkson era. "They're a crucial part of what Top Gear is.
"We'll look at what we have to put in, what we need to put in, and then we'll see what we might want to put in," he continued.
"The first thing I'm going to do is sit down [with the Top Gear production team] and say, 'tell me what you know.'"
In addition to confirming "100 percent" that a woman would feature on the new presenting line-up, Evans said the popular Star in a Reasonably Priced Car segment would remain a Top Gear staple.
But he said it would change and that "bells and whistles" would be added.
Top Gear, he went on, was "a fantastic programme" that was "so rock solid" and had "always been brilliant".
"I've never seen a bad Top Gear," he told Nicky Campbell. "They don't exist."
Evans also reiterated his earlier stated intention that he hoped to remain as host of Radio 2's breakfast show.
Chris Evans has revealed he has received the blessing of Top Gear's former hosts, after it was announced he would be taking over the BBC show.