Jo was brought in as a co-presenter on the early evening slot in May, but was immediately subjected to abuse on social media.
Many other listeners voiced that there was no chemistry between Jo and her co-host.
Last week Simon announced he was quitting Radio 2 after 17 years at the station, after the Beeb confirmed the Drivetime show was being axed in its current format.
Jo, who will now present a brand new show in the 7-9pm weekday slot, says the last six months “have been quite something”.
Writing in an Instagram post on Monday evening she added that “what doesn’t kill you makes you stronger”.
She wrote: “I got into radio because I was obsessed with music, bands and gigs and that’s never gone away. It’s impossible to suppress a passion for good music & it’s going to feel good making new musical discoveries and sharing them with everyone on the new show.
“The last six months have been quite something, I couldn’t have tried harder or cared more about the show Simon & I did together. Some of the stuff that’s been said on social media has meant that some days it was hard to walk out of my front door, let alone present a radio show. But what doesn’t kill you makes you stronger etc etc. Onwards and Upwards!”
After announcing his departure from Radio 2, Simon also took the opportunity to defend Jo over the “appalling” abuse she had experienced and called for “civility”.
Meanwhile, on Monday it was announced that Sara Cox will be presenting the all-new Drivetime show.
Speaking about her new job, Sara said: “I’ve been proud to be part of the Radio 2 family for a few years now and the opportunity to present such a big show as Drivetime - playing fantastic music and hopefully making people smile as they cook tea or head home after a day’s graft - is the icing on what is already a very brilliant cake.
“I’m beyond chuffed to be given this role and to directly quote my mum on hearing the good news, it is indeed ‘fandabbyruddydozy’.”