The Trainspotting author, 63, popped the question to partner Emma Currie on Tuesday.
He told fans online: "My god. She said yes. P***ing wet day in Scotland but she said yes. So f*** everything else. Never been so happy."
The pair met on the street in Leith-born Welsh's home city during lockdown two years ago and their romance blossomed.
Celebrity friends including Line of Duty's Martin Compston sent Welsh congratulations. He wrote: "Yasss big man on ye go."
Singer Lisa Moorish posted: "YESSSSS!! Wonderful news, congrats."
Welsh, who split from his second wife in 2017, had tweeted of the Covid romance: "Was great to be able to take things slowly, with distanced walks and talks. Like an old-fashioned courtship."
He recently revelaed that he is paid even when his novels are stolen from shops - because the stores have to cover the cost to publishers.
The author wrote Trainspotting 1993 and it went on to become a major British film starring Ewan McGregor and Kelly Macdonald.
The gritty drama about a group of heroin addicts in Edinburgh is often cited as the most shoplifted book in Britain.
It spawned a sequel, T2: Trainspotting, featuring the original cast.
The first Trainspotting is often quoted by actors, musicians and authors as having a major influence on their career.