Bongino was a member of the Trump communications team, and all that entails, good and bad. He and Dan Scavino were the authors of a lot of Trump's more infamous tweets.
As the article notes, he's had a podcast for a while now. Being a guy who's never been comfortable with the Trump style that Bongino cultivated, I don't listen so I can't really give you an assessment myself.
As for Westwood One, they are one of the two big players in talk radio, the other being iHeart (iHeart has Beck and Hannity, and also did Limbaugh). Mark Levin is their star host; Chris Plante is also on their roster. They also syndicate Ben Shapiro and Michael Knowles (Knowles was a substitute for Limbaugh near the end), who like Bongino were podcasters before jumping to syndication. So while iHeart is going to continue with the Limbaugh reruns for a couple more months, Westwood One is going to have the clout to put Bongino's new show on a lot of Limbaugh's former affiliates; it is a sister company to Cumulus Media, which owns a large number of Limbaugh affiliates.