The League One club were desperate to retain Darikwa, but were ultimately unable to convince the ambitious defender to stay after he became aware of Burnley's interest.
The 23-year-old spent five seasons with Chesterfield, coming through their youth ranks to cement his place as a key member of the first-team squad.
"Dean Saunders [Chesterfield's manager] tried to persuade Tendayi to agree a new deal, but he was adamant that he wanted to leave and submitted a couple of transfer requests," the club's statement read.
"I can appreciate Tendayi's position because he is keen to further his career by playing in the Championship.
"We were left with the prospect of trying to keep an unsettled player for the season, knowing that we would lose him for nothing at the end of the campaign, so we felt that we had to secure the best fee possible in order to move on and grant Tendayi his wish of playing Championship football."
Having just been relegated from the Premier League, Burnley will be considered one of the favourites to win promotion from the Championship this season and Darikwa could find himself playing in the England's top division sooner rather than later.