Nathan Evans track Wellerman, remixed by 220 Kid and Billen Ted, also dethroned Olivia Rodrigo's Drivers License after nine weeks at the summit.
Mr Evans, 26, said: "We've done it. Unbelievable, I'm speechless. Everybody's support has been absolutely fantastic, thank you each and every one of you. We made it."
Producer 220 Kid added: "Official number one single. I can't believe it. It's a dream come true.
"No matter how much goes wrong, or how many obstacles you reach, as long as you overcome them, you will eventually get there.
"The support on this record has been unbelievable. It's really been magical. Thank you so much."
Their track fended off competition from rappers A1 & J1 at number two, with Latest Trends and Patience by KSI featuring Yungblud and Polo G at number three.
Mr Evans quit his job as a postman earlier this year after helping to kickstart a viral craze of sea-shantying on TikTok and signing a record deal with Polydor Records.
Famous names including Andrew Lloyd Webber, Ronan Keating and Gary Barlow also joined in with the trend and recorded their own sea shanty covers.
Wellerman was boosted by Mr Evans' first TV performance of the track on last week's episode of Ant and Dec's Saturday Night Takeaway.
On the albums chart, singer-songwriter Tom Grennan landed his first number one album with Evering Road.
His debut album Lighting Matches reached number five in 2018.