Boyd had fallen down the pecking order at the KC Stadium after Hull brought in Robert Snodgrass and Tom Ince during the close-season.
The Scotland international will now aim to earn regular first-team action at Turf Moor, as Sean Dyche's side bid to preserve their Premier League status.
Hull initially signed Boyd on loan from Peterborough United midway through the 2012-13 season, before completing a permanent deal for the player at the end of the campaign.
He made 30 Premier League appearances for Steve Bruce's men, scoring twice.
Burnley boss Dyche spoke of a desire to bring in reinforcements following Saturday's 0-0 draw with Manchester United, which saw the newly promoted club pick up their first point of the campaign.
Matt Taylor has started on the left flank, Boyd's regular position, in each of Burnley's league matches this term.
