With his previous contract set to expire next summer, McBurnie has now extended his stay in south Wales until 2021, with the option of a fourth year.
He scored nine goals in 17 appearances at Oakwell last season, which attracted the attention of a number of clubs across the United Kingdom.
Following Swansea's relegation to the Championship, McBurnie could be a huge asset for the Swans next season as they look to bounce back to the top tier of English football at the first time of asking.
Speaking to swanseacity.com after putting pen to paper, McBurnie said: "I am delighted to sign the new contract.
“It’s been a long time coming, but after coming back and seeing the plans for this season, and speaking to the gaffer and everyone involved, I think it’s the perfect thing for me to do at this time in my career. I’m buzzing to get it sorted.
“It’s a time in my career where I need to be settled and find a home. I need to be with my family and concentrating on my football.
“The club have shown faith in me with this contract and I have shown faith in the club. Hopefully it can be mutually beneficial and we can work well together.
“For me it’s now about trying to play as many games as possible and trying to help the club as much as possible.”
With Swansea looking to regain promotion to the Premier League, McBurnie remained coy on his targets for the upcoming season.
“We are not going to put any big shouts out there. It’s not about needing to do this or needing to be there at a certain time,” McBurnie said.
“There’s a new manager in place and new staff and I think there will be a lot of new boys coming in.
“After a tough season last year, it’s about rebuilding as much as possible and getting back to the way we like to play – the Swansea Way. We will see where that takes us.”