The 22-year-old forward becomes League One side Orient's newest addition after emerging as one of six clubs at that level interested in the striker before his contract situation at Spurs was resolved.
Head coach Richie Wellens has already nicknamed his new signing the club's "Great Dane," reflecting the level of expectation attached to a player considered one of Tottenham's most promising academy graduates of recent years.
"He became available late in the window and he's someone with huge potential as a young player," Wellens told the club's official website. "We hope and believe that we can help him fulfil that potential.
"He's had a few different loans, and experienced different clubs. We're now giving him a home and if he can come here and feel the love, and have a really good season, he will show the top talent he is."
Scarlett said he was relishing his first permanent move away from Tottenham.
"I'm very happy to be here and I can't wait to get started," he said. "I want to play and help contribute with goals. It's my first permanent transfer, and I'm excited to come into the next chapter of my career."
A product of Tottenham's academy, Scarlett made his first-team debut at just 16 against Ludogorets in the Europa League in November 2020, becoming the youngest player ever to appear for the club in a competitive match.
He went on to make 27 senior appearances for Spurs in total, scoring once, with loan spells at Portsmouth, Ipswich Town, Oxford United and, most recently, Scottish side Hibernian along the way. He now turns his attention to finding regular goals in League One.
Tottenham's relationship with Orient stretches back years, most notably through Harry Kane's own formative loan spell at Brisbane Road, and the two clubs' history together will have offered some reassurance to Spurs as they sanctioned Scarlett's exit in the final year of his contract.
Having shown flashes of his potential during loan spells across the EFL and a memorable winning goal against Rangers while at Hibernian, Scarlett will now be expected to translate that promise into a consistent goal return at his new permanent home.