They beat top seeds Marcelo Melo and Ivan Dodig in the rain-interrupted final 7-5 7-6 (7-4) on Saturday.
In just their second tournament, the pair secured their first crown together without losing a set all week.
It is Nestor's 89th career title and Inglot's second on home soil, as they prepare to face Andreas Seppi and Fabio Fognini in round one at Wimbledon.
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Inglot, 30, told BBC Sport: "It doesn't get much tougher than playing these guys, so to get a win against that calibre of team before Wimbledon was a big confidence-booster."
Despite failing to take a match point at 7-5 5-4 moments before play was suspended for rain, the pairing managed to close out the match in dominant fashion at the Nottingham Tennis Centre.
"With our quality, you have to go to these tournaments believing you can win," Inglot continued. "We did well to hang in there, especially after the match point and coming out after the rain delay. We came out very fast and that was big for us."
Nestor, who is the only doubles player to have won more than 1,000 matches on the tour, said: "It's important to get matches in before a big tournament like next week and that was our goal before coming here.
"It's great that we were able to do that, and we feel a lot better about our game heading into Wimbledon now."
The 43-year-old added: "We have a tough draw, but we beat some very good teams here and there's no reason why we can't do the same there. This was a great tune-up before Wimbledon."
American world number 38 Steve Johnson claimed his maiden ATP title on Saturday, beating second seed Pablo Cuevas of Uruguay 7-6 (7-5) 7-5 in the singles final.
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Britain's Dom Inglot won the Aegon Open Nottingham doubles title alongside Canadian partner Daniel Nestor.