Senna's family sent a helmet used by the three-time champion in 1987 to give to Hamilton when he earned a 65th pole, which he did in Canada on Saturday.
"It is the most special thing I have, beyond all trophies," said Hamilton.
"As I kid I thought maybe one day I can get to Formula 1 and emulate Ayrton. To equal him; I just can't believe it."
Hamilton has long since surpassed Senna's record of 41 wins - he did so at the 2015 Japanese Grand Prix - and now has 55.
In both poles and wins, he now lags behind only seven-time champion Michael Schumacher, who claimed 68 poles and 91 victories.
Asked whether surpassing Senna's marks meant more than Schumacher's, Hamilton said: "I haven't got to the 68 of Michael so I can't really say. I can't look that far ahead at the moment.
"Ayrton was the guy I noticed from the beginning. I think it was the colour of the helmet. So I am honoured to be honoured by that family.
"To think that I am that close to Michael's record is incredible - I plan on getting there but that is all ifs and buts."
Hamilton, who repeatedly looked at Senna's helmet as he sat in the post-qualifying news conference, said the achievement was even more special given it happened at one of his favourite races - where he claimed his first pole and win back in his debut season of 2007.
"I knew 65 was there and waiting; I knew Montreal has been a beautiful place for me," he said. "I thought if I was going to get that special pole anywhere, it was going to be here.
"But you can only hope it is going to go well, and often it doesn't.
"The lap started perfectly, very smooth, no mistakes, built it up and then the last corner which has always been a strength of mine."
He added: "I am honoured to be among those great drivers, the legends. Ultimately just very proud.
"It wouldn't be possible without all the work from my family.
"This is just the tip of the iceberg. No-one knows how hard we worked to get here. I am proud to have got the Hamilton name here. If this was my last day in the sport, the Hamilton name will remain there forever."
The helmet Hamilton was given is a replica, for travel and insurance reasons, but he will be receiving a genuine helmet that Senna used at a later date.
But Hamilton said he was expecting a tough battle in the race with his title rival, Ferrari driver Sebastian Vettel, who qualified second and leads him by 25 points in the championship.
"Ferrari are very, very strong in the races," Hamilton said. "It was a very close battle last year between us and I can only imagine this year it is going to be pushing all the way to the end.
"We have a car that is not working everywhere. It is a great car but it is a trickier car to set up.
"It appears the Ferrari is an easier car. It works everywhere.
"It puts a lot of emphasis on us pulling together more, using every engineer to the absolute max is key.
"Since I have been with this team, I have never seen such great teamwork. We are all talking more than ever and it is great to see the fruits of that hard work.
"It is going to continue to be a tough, tough race between the Ferraris and us. Today showed we can have an answer."
German Vettel, who has three wins this season, was just 0.330 seconds behind the Briton and is in a confident frame of mind about his challenge in the race itself.
He said: "We always expect Mercedes to be quick, especially in the last segment (of qualifying), but today Lewis just did a better job.
"I expect a close race. It has been close everywhere except maybe Monaco. It is unfair to say one was quicker than the other, we were within the same 0.1secs. So, looking forward to it."
Lewis Hamilton says being presented with one of Ayrton Senna's helmets for equalling the Brazilian's pole record means more to him than any trophy.