Johnny Russell will undergo a medical at Derby on Monday after the striker agreed personal terms with the Championship club.
Dundee United accepted a bid of about £750,000 for the 23-year-old, who had a year of his contract to run.
"The transfer is expected to be concluded after the player has completed the necessary formalities early next week," said United.
Russell scored 20 goals in the 2012-13 season.
The Tayside club added that they are "working extremely hard to bring in quality new players with a view to strengthening the squad".
Former Dundee United manager Peter Houston told BBC Scotland that he believes a move would benefit Russell and United.
"It's good money for them," said Houston. "He's going into the last year of his contract and they might get nothing at the end of next season if they don't move him on.
"Johnny has got to decide if it's a good move for him.
"One thing I'll say about Derby County, having been down there at their training ground, it's absolutely superb. They have a fantastic stadium and a great core of supporters. It's a big club and much bigger than Dundee United.
"So, Johnny has to go see that, speak to the manager, and if they've agreed terms, he has to look at the situation and see what's best. I know Celtic have shown an interest according to the newspapers, so perhaps he's holding off for something like that.
"But if he chooses Derby county, he's choosing a big club."
Italian outfit Catania had repeated offers for Russell rejected, while other Championship sides have made recent enquiries about the product of United's youth system.
Dundee United chairman Stephen Thompson has been open about his intention to sell Russell this summer while he is still under contract.
Huddersfield Town and Sheffield United also made unsuccessful moves for the player, in August and January, respectively.