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Because of the scale of his win, he was able to return to his coalition with the Independent Greeks (or ANEL), a small party, rather than any of the country's centrist or centre-left blocs.
Among the new ministers Tsipras has appointed is Dimitris Kammenos, a politician for the Independent Greeks, Syriza's coalition partner.
He's now the deputy minister for infrastructure, transport and networks.
Unlike Syriza, which is on the radical left, the Independent Greeks (or ANEL) are right-wing and nationalistic, while sharing an anti-austerity viewpoint.
But Kammenos goes much further than right-wing and nationalistic - he's got a back catalogue of awful and conspiratorial comments about Jewish people.
Most recently, Dimitris Kammenos posted a picture on his Facebook page which changed the words "arbeit macht frei" over the gates of the Auschwitz concentration camp to "we're staying in Europe."
A blog that covers anti-Semitic incidents in Greece has a couple of other similar comments from Kammenos.
Kammenos has deleted his Twitter account, where many of the particularly grim comments were made.
On Twitter, The Greek Analyst and journalists Damian Mac Con Uladh and Loukia Gyftopoulou have catalogued some of the new deputy minister's posts before his account disappeared, which you can see below.
"This case smells like 9/11 to me." New deputy minister Dimitris Kammenos on #MH17 in 2014 https://t.co/ylWXvLVwyl pic.twitter.com/5rw9Vthnwy
- Damian Mac Con Uladh (@damomac) September 23, 2015
"Fascist-held EUNew Germano-Nazi EU"2014 Facebook post by new deputy minister in Greecehttps://t.co/N2L1yGhXSX pic.twitter.com/PyJPmuQHiQ
- Damian Mac Con Uladh (@damomac) September 23, 2015
#Tsipras just made this man a Minister in the Greek government. No words. pic.twitter.com/A7b37sqy4R
- The Greek Analyst (@GreekAnalyst) September 22, 2015
New #Greece Minister said ON 9/11/2013: 'Don't forget, no Jew went to work this day out of the 2,500 working in WTC.' pic.twitter.com/mGfZxxOhAd
- The Greek Analyst (@GreekAnalyst) September 23, 2015
The jew-hating Ind Greeks MP who infamously tweeted the below is seemingly in the cabinet of #Greece's leftwing gov pic.twitter.com/iLpAsStrJf
- Loukia Gyftopoulou (@loukia_g) September 22, 2015