The song, which has been a smash hit on TikTok, is set to be the highest new entry on the chart, according to the official first look, based on preliminary sales and early streaming reports.
Evans, 26, from Airdrie, Scotland, has quit his job as a postman after kick-starting a new viral craze of sea-shantying on TikTok (dubbed ShantyTok) and signing a record deal with Polydor Records.
Evans told the PA news agency: “Back in the day when the shanties were sung, it was to bring everybody together, to keep them all in time, to keep the morale high.
“Especially in this time when everybody’s stuck at home, they’re doing their remote working – they can join in, and it kind of brings everybody together.
“So I think it’s just kind of brought it into this day and age. It makes it feel like you’re all united.”
Wellerman is a cover of Bristol group The Longest Johns’ 2018 song, which also entered the Official Top 40 just last week.
Evans has released his own take on the shanty, plus a dance remix produced by 220 Kid and Billen Ted, which is tipped to enter the charts at number four.
Wellerman is the most downloaded song of the week so far, two days into the tracking week, the Official Charts Company said.
The Official Chart: First Look, which airs on BBC Radio 1 today between 6pm and 7pm, offers a first glance of the top 20 ahead of Friday’s Official Singles Chart Top 100.