Miedema had already won the PFA Player's Player of the Year award, as voted for by her peers, but Parris scooped the FWA prize by a single vote after an 11-10 split in the 'expert panel'.
The voting was a two-stage process and Beth Mead, Danielle van der Donk, Leah Williamson (all Arsenal), Magdalena Eriksson, Erin Cuthbert, Karen Carney, Fran Kirby (all Chelsea), Georgia Stanway (Man City), Lucy Bronze (Lyon) and Toni Duggan (Barcelona) all received votes at the first stage.
Parris had enjoyed a fine individual season, scoring 19 Women's Super League goals as her club battled Arsenal - who finally secured the trophy on Sunday - in a thrilling title race.
Her tally broke the previous record for goals in a single WSL season, with only Miedema (22), managing more goals this season and setting an even higher standard.
Parris, who could yet finish the campaign with an FA Cup winner's medal, has also become a crucial player for England ahead of this summer's World Cup in France and has already tasted some international glory in 2019 after the recent SheBelieves Cup triumph.
The 25-year-old is only the second player to win the FWA Women's award after Chelsea star Fran Kirby landed the inaugural prize this time last year.
Furthermore, Parris' Manchester City colleague Raheem Sterling has won the men's award, making it a double triumph for the north west club.