The financial terms of the deal were not disclosed.
Tilbury, who founded the beauty brand in 2013, will continue on as chairman, president and chief creative officer of the brand and retain a minority stake in the company. Demetra Pinsent will remain in her position as chief executive officer.
BDT Capital Partners, financial advisor to Puig, has also made a minority investment in the cosmetics brand.
Stay tuned for updates on this developing story.