The new operator's parent company is a partnership between Aberdeen-based firm FirstGroup and Italy's Trenitalia.
Avanti's first train left Euston for Manchester on Sunday at 08:10 GMT and arrived three minutes late, according to the National Rail app.
It replaces Virgin Trains, which was Britain's longest-running rail franchise after 22 years of service.
The end of the Virgin Trains franchise comes after Virgin Group and Stagecoach had their bid to continue running trains on the line disqualified by the Department for Transport (DfT) in April because they did not meet pension rules.
The companies are suing the DfT over its decision.
At the time, Sir Richard Branson said he was "devastated" by the disqualification.
Customers who had train tickets booked with Virgin Trains for upcoming journeys will be able to use them on Avanti West Coast, the operator said.
The new operator said it would introduce a range of passenger improvements, including 263 more weekly services by 2022, when 23 new trains will begin service.
The existing fleet of Pendolino trains will be refurbished - promising 25,000 new seats, more reliable wi-fi and better catering.
Avanti West Coast has taken over from Virgin Trains as the operator running the West Coast Main Line.