The 28-year old Jamaican international will join the Clarets on January 1 after signing a pre-contract agreement.
Richards, who was recently traded to Vancouver from New York Red Bull, will bring plenty of pace and skill to the Turf Moor line-up according to manager Eddie Howe.
"We are delighted to have signed Dane, who is a player we have been tracking for a while,” Howe said.
"I watched him at New York, where he played for a number of years and he is someone who has all the attributes we are looking for to add to our squad.
"He is quick and direct, has a real turn of pace and I think he will be joining us at a good time in January, hopefully to give us a push in the second half of the season.
"He has good international experience, he is a good age and we're looking forward to adding him to the squad."