The 21-year-old French striker had been training with city rivals Hibernian after leaving Albion this month.
He had joined Stirling on amateur terms in November after exiting French fourth-tier outfit Dieppe.
"I enjoyed my time at Stirling Albion," he told Hearts' website. "I had good moments with them."
Bikey added: "I'd like to thank them and their fans for helping me when I first came to Scotland."
Hearts say the striker, who played four times for Dieppe after starting his career with Nantes, is available for Sunday's Scottish Premiership match with Celtic.
The delighted Frenchman has set his sights on breaking into the first team at Tynecastle.
"This is a new challenge for me," he said. "It's a big club with a big stadium and it's a Premiership team, so I'm very happy to play for Hearts.
"It's a very big opportunity for me. This is my first time at a full-time professional club, so it's a good opportunity for me.
"Playing in the lower leagues has been hard, but I will try every day, I will learn and it's good for me.
"I'm very excited to play in front of thousands of Hearts fans and I hope to score goals for them and make them happy."
Stirling manager Dave Mackay had earlier told his club's website that he knew Bikey would leave at the end of his short-term deal at Forthbank Stadium.
"We are sorry to see Dylan go," he said. "He has obviously made a big impact and we would love to have kept him for longer."
Hearts head coach Ian Cathro are also being linked with a £170,000 deal for Anorthosis Famagusta forward Esmael Goncalves, who previously worked with Cathro at Portuguese club Rio Ave.
However, the former St Mirren player is unlikely to arrive until Monday, with the Cypriot club trying to sign a replacement before allowing the 25-year-old to leave.
Cathro said of his search for an experienced striker: "It's not something which has moved any further than where it was the other night.
"The whole process that we have trying to find that player, not specifically the one mentioned, but I talk about that player which gives us options in attack.
"We are continuing to do our work in a number of areas and, until we can bring the correct one to a close, there is no more news from us."
Dylan Bikey has signed for Hearts and thanked Stirling Albion for helping him win a contract after nine goals in nine games for the Scottish League Two club.