Norris, 17, set the second fastest time behind championship leader Sebastian Vettel's Ferrari at the Hungaroring on Wednesday.
McLaren racing director Eric Boullier said Norris "impressed us all with his maturity, professionalism and speed".
"He's certainly an asset to our test-driver line-up - not to mention a potential star of the future," he said.
"His feedback with the engineers has been valuable and accurate."
Norris' fastest lap of one minute 17.385 seconds was 0.164secs quicker than the qualifying time of double world champion Fernando Alonso in the McLaren at the Hungarian Grand Prix on Saturday.
But the times cannot be directly compared because Alonso was on slower tyres, track conditions were different and the specification of the car Norris was using is not made public.
Norris, who is a front-runner in the European Formula Three series, said on his Twitter feed on Thursday: "How insane was that? Thanks, McLaren."
McLaren replied: "Was totally mega, Lando."
After the test, Norris said in a McLaren statement: "Getting used to the car was a bit of a challenge at first, but by the end of the day I felt very comfortable. I got a lot of laps under my belt and I really enjoyed the experience."
Another British rising star was driving at the test - Mercedes young driver George Russell. The 19-year-old was eighth fastest without having the opportunity to go for headline lap times on the fastest tyres like Norris.
Russell, who races in GP3 this season, tested the 'halo' head protection device which will be used in F1 for the first time next season and said that he had no problems with it - and that in some circumstances it aided visibility.
"I had a much better view with the halo than I expected," he said. "When the sun was coming down at the end of the day, it blocked the sun from my eyes.
"From a driver's perspective, the visibility is completely fine. The only hindrance could potentially be seeing the start lights.
"Getting in and out of the car with the halo takes a bit of experience. I struggled initially, but after a few trial runs I was fine."
Rising British star Lando Norris had an impressive first test in a current Formula 1 car with McLaren.