Leeds announced earlier this week that the English Football League had approved the takeover by the American investment group.
Chairman and majority shareholder Andrea Radrizzani agreed to sell his controlling stake last month and the deal, which valued the club at around £170 million has now been confirmed.
49ers Enterprises, which owns NFL franchise the San Francisco 49ers, has steadily increased its stake in Leeds since becoming a minority shareholder in 2018.
Three-time major winner Spieth is one of a number of high-profile sportsmen to invest in the group, along with fellow American golfer Justin Thomas, Olympic swimming great Michael Phelps and NBA star Russell Westbrook.
Competing at the British Open in Hoylake, Spieth said he had become a fan of the English club, who will be playing in the second-tier Championship this season.
"It was brought to me last fall by a couple of guys that know the 49ers group really well, so I've been looking at it since then, cheering them on this year, and then when they were relegated, I was going to see kind of what the new restructured deal was," he said.
"It was going to take a lot for me not to get involved. I had already gotten emotionally involved. Yeah, I'm excited. Myself and JT (Thomas) we've been kind of texting each other for six months now every game and even the other games we needed teams to lose and stuff like that.
"It'll be fun to keep track, hopefully get back into the Premier League."
Spieth, who won the British Open at Royal Birkdale in 2017, carded a two-under-par 69 in his first round at the Royal Liverpool course on Thursday.
