Posting the same picture on their individual Twitter accounts, she wrote, "I'm engaged to him" and he wrote, "I'm engaged to her."
Cox, 50, and McDaid, 37, were first spotted out together in December of last year after they were introduced by rocker
In April, Sheeran let it slip to the Mirror that his pals were already living together.
"They get on really well and are genuinely good friends, pardon the pun," he said at the time.
Cox's ex-husband David Arquette had given McDaid his stamp of approval in February in an interview with Wendy Williams where he called the musician "amazing" and a "great guy." McDaid plays piano and guitar and sings backup vocals for alt-rock band Snow Patrol, whose hits include "Chasing Cars."