The firm now owns a total of almost 516 million shares of Sky, according to an official statement from the London Stock Exchange. It says it will continue to make further purchases of Sky shares at a price of £17.28 ($22.60) per share.
"Comcast Bidco will continue to acquire Sky Shares in the market from eligible shareholders outside the United States at up to and including £17.28 in cash for each Sky Share," the statement said.
Comcast Bidco is an indirect, wholly-owned subsidiary of Comcast Corp.
Comcast said eligible shareholders outside the United States interested in selling their stake in Sky should contact brokerage Bank of America Merrill Lynch.
Comcast prevailed over Twenty-First Century Fox after a protracted bidding battle, which was drawn to a close on Saturday in a showdown that saw Comcast make a takeover offer of about $40 billion for Sky.
Fox, which is itself set to be bought by Disney, is currently the biggest shareholder in Sky, owning 39 percent of the company. Sources told CNBC that Fox may sell its stake in Sky to Comcast in return for the latter's 30 percent ownership of TV streaming platform Hulu.
On Monday, The Sky Independent Committee recommended that its shareholders accept the offer from Comcast "'immediately" as it was in the best interest of the company.
"As the price of the Comcast Offer is materially superior, it is in the best interests of all Sky shareholders to accept the Comcast Offer," the committee said.
Analysts told CNBC that U.K. pay-TV provider Sky is seen by Comcast as a valuable asset due to its European exposure and strength in digital media and sports programming. Sky owns TV streaming company Now TV and holds the rights to broadcast Premier League soccer games.
Matt Halbower, chief executive of Pentwater Capital, who sold his 1 percent share in Sky to Comcast on Monday, said the extra debt Comcast would take on was insignificant compared to the international expansion the Sky acquisition would bring to the company.
"This is a platform for Comcast to grow internationally," Halbower said. "They wanted to grow in the United States. They were thwarted when the Department of Justice and the FCC (Federal Communications Commission) refused to allow them to buy Time Warner Cable, so now they have to look overseas and Sky is a great platform for them to be able to build overseas."
—Disclosure: Comcast is the owner of NBCUniversal, parent company of CNBC and CNBC.com.