The club announced the signings through its official channels, welcoming both players from Empoli.
Olivieri, born in 2010, and Perillo, born in 2009, both won the Under-17 title with Empoli last season, with Perillo also becoming European champion with Italy's Under-17 side.
The club's statement expressed a warm welcome to both players as they join Atalanta's youth setup.
While that business was completed at academy level, Atalanta are also being linked with reinforcements for the first team, with reports from Brazil naming Corinthians midfielder Breno Bidon as a candidate to replace Ederson.
Ederson is close to completing an official move to Manchester United, prompting Atalanta to explore options in South America, according to Brazilian outlet ESPN.
Bidon, 21, is a left-footed midfielder who has represented only Corinthians throughout his career, making 131 official appearances and scoring five goals.
ESPN's Brazilian edition reports that Atalanta's scouts have been monitoring Bidon's performances for some time. The report adds that Bidon holds an Italian passport alongside his Brazilian one, meaning he would not occupy a non-EU slot if he moved to Serie A.
Bidon is under contract with Corinthians until 31 December 2029, with a release clause reported at €100 million. According to the same report, Corinthians have yet to receive any official offer for the midfielder.
The two strands of business highlight Atalanta's activity across different levels of the club this summer, with the academy signings aimed at strengthening the pipeline of young talent while the club also looks to address a potential gap in midfield at first-team level.
Olivieri and Perillo arrive with strong pedigree at youth international level, having already tasted success together with Empoli before this move.
The interest in Bidon remains at an early stage, with no formal approach yet made to Corinthians, but his dual nationality and left-footed profile mark him out as a player Atalanta's recruitment staff see as a natural fit for the type of midfielder the club typically targets.
Any deal for Bidon would depend on Ederson's departure to Manchester United being finalised, freeing up both a squad slot and funds for Atalanta to pursue a replacement in that area of midfield.