"Valery Karpin was given a one-and-a-half-year contract to be the head coach," Spartak's billionaire owner Leonid Fedun said on the club's website.
"He has been tasked with winning one of the three trophies - either the Russian league, the Russian Cup or a European cup during that time."
Former Russia international Karpin was named Spartak's caretaker coach last month, replacing Spaniard Unai Emery, who was sacked following a 5-1 defeat by bitter city rivals Dynamo.
Spartak, Russia's most popular and successful club with nine domestic titles between 1992-2001, have also underperformed in Europe this season, finishing bottom of their Champions League group.
However, Spartak headed into the Russian league's three-month winter break on a high after beating Rubin Kazan 1-0 on Monday to end a run of four consecutive defeats.
The win enabled Spartak to leapfrog Kazan into sixth place in the league table, 11 points adrift of leaders CSKA Moscow.
Karpin, 43, had a distinguished playing career with Spartak and Spanish clubs Valencia, Real Sociedad and Celta Vigo but had no coaching experience before becoming general director at the Moscow club in August 2008. Eight months later he fired Denmark's Michael Laudrup as coach and took over the hot seat.
Karpin combined the two jobs for three years before resigning in favour of former Valencia coach Emery in May despite Spartak finishing last season in second place and qualifying for the Champions League.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
