The 20-year-old forward has not featured for the Easter Road side since August with an ankle injury limiting him to just six appearances following the move from Inverness Caledonian Thistle in the summer.
He scored his first Hibs goal in the 2-1 win over FC Santa Coloma in a Europa Conference League qualifier back in July and also featured against Killie in the late stages of a League Cup game at Easter Road.
He found the net nine times for his former club in the cinch Championship last season and joins a Kilmarnock side looking to secure promotion back to the top flight at the first time of asking under new boss McInnes.
McKay, who made his Scotland Under-21 debut against Northern Ireland in June before gaining a second cap against Turkey in September, trained with his new teammates on Thursday and could make his Killie debut on Friday night against Partick Thistle at Firhill.
“It’s a good opportunity for me to come to Kilmarnock with the goal of winning the league and hopefully I can help the team do that," McKay said.
“I’m happy that the manager was keen to bring me in and I can’t wait to get started now. I’m direct, quick and can score goals as well so hopefully I have all the ingredients to show the fans that I can do well on the park.”