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The 24-year-old Scot beat Sweden's Paralympic champion Stefan Olsson 6-1 6-4 on a packed-out court 17.
Reid, who was runner-up in the French Open, adds Wimbledon to the Australian Open title he won in January.
"It's incredible," said Reid. "I'll never forget this moment."
Wheelchair tennis has been played at Wimbledon since 2001 but this year is the first time men's and women's singles have featured.
"To have the opportunity to play singles here is something I've dreamed of for a long time," added Reid.
"And to come here and win it in front of all the people I love: my friends, my family, my coaches, with so much support. It's great."
Reid, who was ranked third in the world at the beginning of the week, hopes his continued success will inspire the next generation of wheelchair tennis players.
"I said at the start of the week I wanted to achieve two things," he told BBC Sport. "First if there were any kids with disabilities for this to inspire them to take up the sport.
"And second was to continue to break down the barriers when it comes to disability sport, to showcase the talent in the sport. The coverage and interest we've had this week, it's been a big milestone and hopefully we can build on that."
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Great Britain's Gordon Reid won his second Wimbledon title in as many days by adding the men's wheelchair singles to the doubles title he won alongside Alfie Hewett on Saturday.