The 39-year-old Croatia captain has spent the last 13 seasons with Real Madrid and helped them win six Champions League titles after a four-year spell at Tottenham earlier in his distinguished career.
Swansea have not disclosed how much Modric, who won the Ballon d'Or in 2018, had invested but he expressed excitement at the chance to use his knowledge to help the Welsh outfit.
Modric said on the club's website: "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's main focus right now is on Real Madrid's Champions League quarter-final second leg at home to Arsenal on Wednesday, but his contract at the Bernabeu is set to expire at the end of this season.
His decision to invest in a football club follows team-mates Kylian Mbappe and Vinicius Junior doing likewise at Ligue 2 outfit Caen and Portuguese side FC Alverca, respectively.
Swansea are owned by Andy Coleman, Brett Cravatt, Nigel Morris and Jason Cohen, a group who assumed majority ownership from Jason Levien and Steve Kaplan last November.
"I am excited that Luka has come on board as an investor and co-owner," Swansea chief executive Tom Gorringe said.
"There is no better role model in the game for our players, from the academy right through to the first team."
Swansea's most recent accounts, released last month, showed a pre-tax loss of $32 million for the financial year ending June 2024.
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