The cross-channel train service turns 25 on November 14, and the app-based button will be available on several dates before then.
A free glass of fizz will be served to the first 25 passengers on selected trains who activate the feature, which launches on Tuesday to mark 100 days until the big anniversary.
The button is available on the rail operator's smartphone app today and then every Friday for the rest of August.
It will be available on the 5.01pm departure from London to Paris, the 5.13pm departure from Paris to London, and the 5.16pm departure from London to Brussels, Rotterdam and Amsterdam.
Around 11 million passengers travelled with the firm in 2018, up 7 per cent on the previous year.
Eurostar's chief customer officer Marc Noaro said: "For 25 years Eurostar has provided customers with a fast, comfortable and enjoyable way to travel.
"We're trialling a new 'press for champagne' button this summer to offer travellers a chance to join in the celebrations and make their trip even more special."