Cripps snatched the lead with three votes in Carlton's heartbreaking round-23 loss to Collingwood to win the AFL's highest individual honour on 29 votes ahead of Brisbane gun Neale (28 votes) and Gold Coast's Touk Miller (27).
He is the first Blue to win the Brownlow since former skipper Chris Judd in 2010.
"Mate, I don't know whether to laugh or cry," Cripps said as he accepted the prestigious medal.
"I loved footy growing up as a kid, and I still remember being at boarding school back in WA, and I used to always ask my mum, 'Make sure you sign me out, give me leave on Brownlow night', because I used to love watching it.
"My older brother Daniel used to sign me out and we always used to watch it together. Mate, it's unbelievable.
"I can't put it into words at the moment but it's a massive honour and I'm absolutely pumped."
Sunday night's count, moved from the traditional Monday night timeslot due to the funeral of Queen Elizabeth II, went down to the wire.
Miller went into the final round with the lead, but failed to poll, while Neale snatched a slender lead with one vote against Melbourne.
But Cripps, in the final announcement of the count, drew the maximum votes for 35 disposals and 12 clearances in the one-point loss to Collingwood that ultimately cost the Blues a finals berth.
Overall, Cripps polled in 13 games and earned the maximum three votes seven times.
He arguably could have added a couple more votes to his tally but received just one for his three-goal, 30-disposal effort against Richmond in round one.
The 27-year-old was also nearly ineligible.
Cripps was suspended after round 21 for a bump that concussed Brisbane's Callum Ah Chee - which would have ruled him ineligible for the Brownlow - but had it overturned at the tribunal.
Cripps, 27, first took the lead in round seven but was pegged back by Neale, who led for much of the count from round eight.
Fremantle star Andrew Brayshaw finished fourth on 25 votes but failed to poll in the final three rounds.
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