The chef has taken over the former Filmore & Union site on Low Petergate, which has undergone a £50,000 refurbishment.
The site seats 35 diners across two floors and offers small plates such as truffled mac and cheese; beetroot-cured salmon; as well as open sandwiches and a brunch menu.
It follows the opening of the first Grön café in Leeds in 2018, which serves vegetarian and vegan dishes.
Healy, who was a runner-up in the 2016 series of MasterChef, also runs Leeds gastropub The Beehive and The Foundry restaurant in the city centre.
“Grön has been such a big hit and the vegan and vegetarian scene is going from strength to strength with more people than ever making changes to their food choices,” says Healy.
“We’re excited to expand further afield and build on the success we’ve already seen in Oakwood.”
Healy trained at Thomas Danby Catering College in Leeds and worked at the original El Gato Negro restaurant in Manchester, as well as London's Terroirs.