The deal sees Rohan Masson-Taylor, who founded the business in 1977, relinquish his majority stake in the company.
While the price of the deal has not been disclosed, the company generated a turnover of around £50m for the year to September 2017.
Cadogan Tate specialises in packing, moving, shipping, storage and insurance for fine art and other high-value possessions. Its clients include interior designers, auction houses, art galleries and museums. It employs approximately 450 people.
Masson-Taylor started out with a Luton van, an office above a Covent Garden wine bar and storage premises in Southwark, but oversaw its growth into an international operation which now includes offices in New York, Los Angeles, Miami, Paris and the Cote d’Azur as well as its headquarters in London.
Last year the company worked on US President Barack Obama’s move out of the White House.
H2 said it will work closely with the existing management team and intends to help the company invest in its storage facilities and open new offices. It added that it aims to “drive the company’s strong focus on providing a premium service”.
Mason-Taylor said: “We chose to partner with H2 based on their good knowledge of our sector and excellent track record built up over 27 years of working with family-owned businesses. Our management team and H2 have developed a strong relationship and we look forward to seeing Cadogan Tate continue to develop and grow.”