The American's New England Sports Ventures (NESV) agreed to buy the Premier League club for 300 million pounds last week but a legal battle between the board and current owners Tom Hicks and George Gillett stalled the deal.
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A High Court judge ruled on Wednesday that the owners, who had tried to block the deal by attempting to sack members of the board, could no longer stop it.
Asked how confident he felt going into the meeting, Henry replied: "Pretty confident" as television pictures showed him clutching a briefcase in each hand as he rushed through the glass doors.
The 18-times English champions have also received a 320 million-pound offer from Singapore billionaire Peter Lim and Wednesday's meeting in London is likely to end with an announcement about who will buy the club.
Henry's NESV company owns Major League Baseball's Boston Red Sox and if they take over the football club, Liverpool fans will be hoping for a similar turnaround in their fortunes as the baseball team enjoyed following their 2002 takeover.
In 2004 the Red Sox won their first World Series since 1918 and they secured the title again in 2007.
Liverpool are sitting in the Premier League relegation zone and players are looking forward to turning things around on the pitch.
"It seems things are nearly sorted off the pitch so we need to start getting them right on it by getting three points at Goodison (Park) on Sunday," Liverpool captain Steven Gerrard said on the club's website referring to the derby at Everton.
"I know how frustrated the fans have been with what has been going on and I can understand their feelings. But we've all suffered in this, especially the supporters, and now it's time for us all to pull together and help move the club forward."
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