The takeover is expected to be completed on Monday.
The consortium, which won the bid to acquire the London side earlier this month, received approval from the Premier League and the British government this week for the sale to go ahead.
"Chelsea Football Club can confirm that a final and definitive agreement was entered into last night to sell the Club to the Todd Boehly/Clearlake Capital consortium," the club said in a statement.
"It is expected that the transaction will be completed on Monday. The club will update further at that time."
Russian owner Roman Abramovich put the club up for sale in early March following Russia's invasion of Ukraine, which Moscow calls a "special military operation".
The sale also needed the green light from the Portugal government after Abramovich became a citizen of the country last year and is under European Union sanctions.
Chelsea had been operating under a special licence issued by the British government since Abramovich's assets were frozen in March and it was set to expire on May 31.
The completion of the sale will allow Chelsea to renew transfer activity as well as permit players to sign new contracts, which was prohibited as part of the sanctions imposed.
Abramovich bought the club in 2003 and helped Chelsea become a dominant force in English football, leading them to five Premier League titles, five FA Cups and two Champions League trophies during his reign.