Sean Dyche's side have agreed a deal to sign the striker after having an offer for Majeed Waris rejected by French side Lorient.
Wells would be the second attacking addition of the week for Burnley, after Chris Wood, following the departure of Andre Gray to Watford.
The Bermudan striker scored 49 goals in 153 appearances for Huddersfield after joining from Bradford in 2014 and became a very popular figure amongst the Terriers fans.