Fury recorded his message to the Bronze Bomber on video on Friday morning ... thanking him for their trio of amazing fights and hoping he lives it up on his 36th birthday.

"I hope you have a fantastic day with you and your family," Fury said. "And I hope that God blesses you abundantly. All the best. Lots of love from your old pal, the Gypsy King."

Fury also showered Wilder in compliments, calling him a "great, great" and "awesome" fighter.

"All the best," Fury added. "God bless, Wilder. All the best."

The video tugs at the heartstrings a bit ... considering how much the two have appeared to have disliked each other over the years.

Both guys have talked an incredible amount of trash toward each other -- and immediately following their third fight earlier this month, Wilder straight-up told Fury, "I don't respect you."

But, Wilder got over those feelings in the days following the match ... and sent Fury a message congratulating him and thanking him for the fights.

Seems Fury received the note loud and clear -- clearly showing he'd prefer if the two were buddies from here on out.