The legendary Real Madrid and Croatia midfielder has joined Andy Coleman, Brett Cravatt, Nigel Morris and Jason Cohen in the Championship club's ownership group and has promised to use his vast experience in the game for the benefit of the Welsh side.
Modric said: "This is an exciting opportunity. Swansea has a strong identity, an incredible fanbase, and the ambition to compete at the highest level.
"Playing at the highest level, I believe I can provide my experience to the club. My goal is to support the club's growth in a positive way and to help to build an exciting future."
Modric will continue playing for Real Madrid following the ownership move, although his contract with the La Liga side is due to expire at the end of the season.
Swansea stated: "Luka's investment in the club is an endorsement of the club's ambition and vision. He will play a key role in helping the club garner global attention and progress both on and off the pitch."
The club's chief executive Tom Gorringe hailed Modric as the ideal "role model" for Swansea's players and praised the veteran midfielder's "genuine passion" for the improvement of the team.
He said: "There is no better role model in the game for our players, from the academy right through to the first team.
"His endorsement of our ambition and willingness to support us on our journey will be instrumental as we aim to continue to improve our results on and off the pitch.
"In our conversations, he has demonstrated his passion for the club, his knowledge of how we are performing, and a genuine passion to help us improve."