Schär was presented with the association's Player of the Year award while Longstaff won the Young Player of the Year award at a star-studded event held at the Ramside Hall Hotel, Golf and Spa, Durham.
Swiss defender Schär becomes the fourth Newcastle player in a row to win the annual award. Martin Dúbravka was last year's recipient while Jamaal Lascelles and Matt Ritchie were joint-winners in 2017.
In total Newcastle players have won the award 19 times, with Sunderland on 11, Middlesbrough on nine and Hartlepool United's former Magpies forward Joe Allon taking the prestigious trophy home in 1991.
Speaking at the event, Schär told NUFC TV: "It's a big honour for myself. I know I had a great first year here at Newcastle. From the first day, I felt really comfortable. The spirit here is great and the city, along with the fans and to play at St. James' Park.
"For me, it was a perfect year and standing here now this evening is a great honour for myself and for the year I had. "It is nice when you see you have people who like how you play or the way you play. It's recognition for the year I had and the hard work I've done not just in the last year but for the last couple of years."
Longstaff was the unanimous choice for the young player award, which has previously been won by the likes of England goalkeeper Jordan Pickford, Ayoze Pérez and Steven Taylor.
"To win any sort of award is really nice and to be recognised by the press is great as well," he told NUFC TV. "I've really enjoyed the last year. There's been a few ups and downs along the way but I'm still loving every second of it!
"It's been a great year and it's sort of topped off tonight with a nice little award. It's something I'm going to keep, cherish and be able to look back on. For me, it's about kicking on now and trying to get myself in the team more and more and playing well."
Durham Women FC defender Kathryn Hill was presented with Women's Player of the Year while Manchester City and England Women captain Steph Houghton won the North East Personality of the Year award, in association with the Sir Bobby Robson Foundation, which has previously been awarded to Alan Shearer, Jermaine Defoe, Steve Harper, Robbie Elliott and Niall Quinn.
As well as recognising success in non-league football, the North East Football Writers' Association also presented the Bob Cass Award and the John Fotheringham Awards, named after two renowned North East football writers, and recognising outstanding services to football in the region.
Spennymoor-born referee George Courtney, who officiated at the 1986 and 1990 FIFA World Cup finals, and former Sunderland captain Kevin Ball were the recipients of the respective awards.