The 18-year-old centre-back came through the youth system at Stoke City and impressed during a trial with the Latics.
The contract also includes the option of an extra year that Oldham can take up after this season.
"He is really athletic, only 18 and definitely one for the future," boss David Dunn told the club website.
"He has a lot of very good attributes and we spoke to Mark Bowen at Stoke City about him so we have decided he is a good young signing for us."
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According to its website, both the 32GB and 64GB models are "currently unavailable", and Amazon says it has no plans to replenish its inventory.
It follows reports of lay-offs at the US company, after the phone failed to resonate with consumers.
Amazon has not responded to requests from the BBC for comment about its plans for the phone.
Launched with much fanfare in June 2014, the Fire Phone was Amazon's first foray into the smartphone market.
The main selling point was its "dynamic perspective" camera, which can track the user's movements and give the impression of depth and 3D.
It also includes a 24-hour customer service tool and an in-built encyclopaedia called X-Ray.
But the rollout quickly faltered, as reviewers took against the phone, and Amazon cut its price drastically last September.
In October 2014, the company revealed it had suffered a $170m (Â£110.5m) writedown "primarily related" to the gadget.
And last month, the Wall Street Journal reported it had laid off "dozens" of Fire Phone engineers at its Silicon Valley research-and-development lab.
Stuart Miles, editor and founder of technology news website Pocket-lint, said he was not surprised by the decision to pull the phone.
"The phone industry is incredibly competitive, and it's very foolhardy for any company to believe you can come in on your first product and make a difference.
"Amazon obviously believed it could launch something, which unfortunately didn't gain any excitement.
"The dynamic perspective camera was pretty much seen as a gimmick which didn't really add anything to the overall experience."
Amazon is still selling its tablets, such as the Kindle and Fire. On Tuesday, the Wall Street Journal reported Amazon planned to launch a cut-price $50 (Â£33) tablet this Christmas, along with new tablets with 8in (20cm) and 10in screens.

The 28-year-old Italian, who joined the Black Cats from Arsenal in 2013, was injured during a training session.
Manager David Moyes said he would "definitely" look to make a signing as Jordan Pickford, 22, is his only fit senior goalkeeper.
Moyes added the club had made a bid for Sevilla midfielder Vicente Iborra.
The 28-year-old joined Sevilla from Levante in 2013 and is a three-time Europa League winner.
Moyes said Mannone's injury gives Pickford "the chance to show what he can do".
He added: "He has a big future ahead of him."
The England Under-21 international is a product of the Sunderland academy and has played for a host of clubs on loan.
He made his senior debut for the Black Cats in an FA Cup tie at Arsenal last season, before making two Premier League appearances.
League One side Oldham Athletic have signed defender Theo Vassell on a deal until the end of the season.
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Online retailer Amazon has stopped selling its Fire smartphone, just 15 months after the handset was launched.
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Sunderland goalkeeper Vito Mannone will be out for at least three months and could require an operation after tearing elbow ligaments.