The Inbetweeners actor proposed to the model earlier this week, reports The Sun.
The pair became parents to baby Harrison in October after dating for just over a year.
His Inbetweeners co-star Joe Thomas has reportedly moved in with his girlfriend, while Simon Bird proposed to Lisa Owens in November.
Simon Bird recently joked that Buckley's son Harrison is a "little b**tard".
Watch Digital Spy's interview with The Inbetweeners Movie stars Simon Bird, Joe Thomas, James Buckley and Blake Harrison below: