The 18-year-old is Michael Laudrup's second acquisition of the January window following David N'Gog's arrival on Monday and joins the club on three-and-a-half-year deal.
King has broken into the first-team picture at Tynecastle during the current campaign, making three senior appearances, including a start in a 2-0 defeat at Celtic last month.
The Scotland Under-19 international will initially join up with Swansea's development squad, but will be keen to make an impact as soon as possible.
And Hearts wished their youth product all the best upon confirmation of the move.
"We would like to wish Adam well," read a statement on the club's website. "This is a great opportunity for him and we will follow his progress with Swansea with interest."
Swansea have been in dire need of central midfielders of late, with centre back Jordi Amat having to play out of position to cover for the absence through injury of players such as Jonjo Shelvey, Jose Canas and Jonathan de Guzman.
