King, 20, and 19-year-old Buchanan have been tied down for two more years, while Oliver, also 19, has penned a 12-month extension
The new agreements are reward for impressive campaigns. Winger King made 33 appearances and scored nine goals while strikers Oliver and Buchanan - voted the club’s Under-20s player of the year - enjoyed loan spells at Stenhousemuir and Cowdenbeath respectively, as well as making 18 first-team appearances between them.
Neilson said: “I’m pleased to get Billy signed up. He’s performed really well for us this year. He’s got a big future at the club and I’m glad to get him tied up.
“Both Gary and Robbie went out on loan this season and did really well. We were desperate to get Gary back from Stenhousemuir and into the first-team squad and get him involved, and he’s done really well towards the end of the season.
“Robbie performed well on loan at Cowdenbeath and I was really pleased with his performances.
“The two of them will be pushing for the first-team squad next season so it’s great to get two of bright, young talents signed up.”
Meanwhile, the Tynecastle club have also confirmed midfielder Scott Robinson - linked with a move to Kilmarnock - will leave the club when his deal expires at the end of the month.