The Morecambe striker picked up the award after netting four league goals in the opening month.
Those included an opening-day double at Ipswich Town and the second in the Shrimps’ defeat of Shrewsbury Town.
In all, the 27-year-old scored six times in seven league and cup appearances as Stephen Robinson’s players adapt to life in League One.
Stockton said: “I am absolutely delighted to be chosen as the August Player of the Month for League One.
“As a team we have had a great start and I am pleased with the goals I have scored so far, but I would not be able to score them without the hard work that the team puts in around me.
“August has been a good month to the club. We came close to three points on the opening day of the season against Ipswich Town, and then beat Sheffield Wednesday on the final weekend.
“There’s still a long way to go but it has been a very good start for the football club.”
Robinson added: “It’s fantastic for Cole, it’s thoroughly deserved.
“He’s worked very hard and some of his goals have been fantastic, as has his all-round play.
“I think that’s improved no end but he’s getting his just reward and I’m sure he will be the first to thank his team-mates - but I’m really delighted for him.”
Also on the shortlist were Oxford United midfielder James Henry, Sheffield Wednesday goalkeeper Bailey Peacock-Farrell and Portsmouth midfielder Ryan Tunnicliffe.
Sky Sports’ EFL pundit Don Goodman said: “The sight of Cole Stockton charging towards them is likely to terrify a few more defenders over the course of the season, with the centre-forward leading the way in the division for ball carries ending with a goal.
“Morecambe are punching above their weight so far this campaign, and Stockton has been a big part of that, the highlight being a man-of-the-match performance on the opening day at Ipswich Town.”
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