Messi, 39, has now become the majority owner of a second club in Spain this year, after the purchase of UE Cornella in April.
The former Argentina and Barcelona forward, who currently plays for Inter Miami, last month agreed a deal to acquire all the shares of Eldense held by a Colombian investment group, the previous majority shareholder.
"Club Deportivo Eldense officially announces the acquisition of the club by Leo Messi, marking the start of a new and exciting chapter in the club’s history, which spans more than a hundred years," Eldense, who were established in 1921, wrote on the club's website.
Eldense will hope that the deal will give them a lift as they sit 19th in the Segunda Division with four losses in seven matches, fighting to avoid relegation.