Stojkovic and Kingson could come face to face at next summer's World Cup in South Africa, as Serbia and Ghana have been drawn in the same group, along with Germany and Australia.
The Serb goes straight into the squad to face Aston Villa on Saturday and manager Roberto Martinez is pleased to have brought in more cover for Kirkland.
"Vladimir is a highly experienced keeper who is the number-one choice in his home country," said Martinez.
"That shows you the calibre of professional we are signing, as a player but also in terms of his character and determination to succeed.
"He will add tremendous competition for places in the goalkeeping department, something which we need everywhere on the pitch."
Stojkovic added: "It is going to be very tough because I know the quality of the goalkeepers already here but every professional trains to play first-team football.
"I am looking forward to the challenge of getting in the team and fighting for a place."
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