Moha, 21, who is now with Stoke City, has joined the Tynecastle club until the end of the season.
Hearts have said he is under consideration for this afternoon’s Ladbrokes Premiership match against Celtic away.
Tziolis, 31, is a free agent after parting company with the Greek Super League side PAOK Salonika.
Primarily a defensive midfielder, Tziolis is vastly experienced with over 60 caps for Greece. He played in the 2008 European Championship and the 2010 World Cup and his CV includes stints in the German, Italian, Spanish and French leagues with Werder Bremen, Siena, Racing Santander and Monaco.
Moha, pictured, is a Moroccan under-23 international who began his career at Espanyol before moving to city rivals Barcelona, where he won the UEFA Youth League in 2013/14.
He joined Stoke City in July 2015 but has yet to play for the first team, athough he was an unused substitute in a couple of Premier League games last season.
He spent the first half of this season on loan at Shrewsbury Town, making six appearances for the Sky Bet League One side.
The Stoke player is Hearts head coach Ian Cathro’s sixth January signing following the arrival of French pair Malaury Martin and Dylan Bikey, and the defenders Aaron Hughes, Lennard Sowah and Andraz Struna.
Cathro is also understood to be close to completing a £170,000 deal for former St Mirren striker Esmael Goncalves, who is currently with Cypriot side Anorthosis Famagusta.
Goncalves previously worked with Cathro at the Portuguese side Rio Ave and is also known to Hearts No.2 Austin MacPhee from the pair’s time together at St Mirren.
The striker played what is likely to be his final match for Anorthosis yesterday, scoring twice in a 4-1 win over Ermis.