Skipp, 17, is widely considered to be one of the most promising talents in Spurs' academy after making an immediate impact during his first season as a full time scholar having progressed from the Under-18s to the Under-23s.
The midfielder is tipped to be nearing a first team breakthrough after impressing during the club's tour of the US over the summer, having featured from the bench against Roma and Barcelona before being handed a starting role in the win over Milan.
Amos, 21, rose through the ranks with Tottenham and has recently gained experience in the Football League with loan spells at both Southend United and Stevenage over the past two seasons.
The 21-year-old started in the middle of the park for all three of Spurs' International Champions Cup games, which paved the way for his Premier League debut in the opening day victory over Newcastle, having made his appearance from the bench with two minutes left to play.
Eyoma, 18, was a regular for the Under-23s side last term and also featured on the US tour, having started alongside Davinson Sanchez in the centre of defence against Milan.
The defender was a member of England's Under-17 World Cup triumph last year, and can also play a role at right back.
Tottenham's announcement of another batch of new signees comes after a host of senior players renewed terms with the club over the course of the year.