Howe revealed after Friday night's 2-1 League One defeat at Colchester that the match was his last in charge of the Cherries.
The 33-year-old said: "I'll be travelling up to Burnley on Saturday to hopefully finalise things.
"I've been loyal to Bournemouth and it's extremely difficult to leave a club that's been close to my heart."
He continued on Sky Sports: "I turned down two other clubs on Tuesday - then Burnley came in two days later.
"I just thought that was too good an opportunity to turn down. I don't lack drive or ambition."
On Bournemouth, he added: "We've had two years of unbelievable success here and I hope the lads continue that and go on to get what they deserve. I leave with great sadness."
Burnley issued a statement on Friday night which read: "We have agreed a compensation package with AFC Bournemouth to allow talks to take place with Eddie Howe over the managerial vacancy at Turf Moor.
"Howe, along with assistant manager Jason Tindall, will travel to Lancashire this weekend to discuss personal terms."