The 47-year-old presenter and Bonkers actress will make her debut on May 12, reports BBC News.
Comedian Carr, who has been on the station for three years, said he had "loved every minute" and was looking forward to "reclaiming [his] weekends".
Tarbuck has stood in on various Radio 2 shows since 2007, including Steve Wright's weekday afternoon slot and Simon Mayo's Drivetime.
She was said to be on the verge of securing her own show in 2009, but nothing materialised.
Going Out With airs every Saturday evening between 6pm and 8pm.