According to the Telegraph, the decision was made by the General Assembly on the Mound in Edinburgh on Saturday, where the motion was passed by 309 votes in favour and 182 against, following of years of debate within the Church.
It means the Church has adopted a position which maintains a traditional view of marriage between a man and woman, but allows individual congregations to "opt out" if they wish to appoint a minister or a deacon in a same sex civil partnership.
The outgoing Moderator Very Rev John Chalmers said: "We cannot go on suffering the pain of internal attacks which are designed to undermine the work or the place of others. It's time to play for the team.
"And let me be very clear here - I am not speaking to one side or another of the theological spectrum. I am speaking to both ends and middle.
"It is time to stop calling each other names, time to shun the idea that we should define ourselves by our differences and instead define ourselves by what we hold in common - our baptism into Christ, our dependence on God's grace, our will to serve the poor and so on."
Co-ordinator of the Principal Clerk's office, Very Rev David Arnott, said: "The General Assembly of the Church of Scotland decided today to allow individual Kirk Sessions the possibility of allowing a nominating Committee to consider an application from a minister living in a civil partnership.
"During a vacancy a Kirk Session may, but only if it so wishes, and after due deliberation, agree to a Nominating Committee accepting an application from such a minister. No Kirk Session may be coerced into doing so against its own wishes. This decision was in line with a majority of presbyteries who voted in favour of such a move."
The Assembly will be asked on Thursday to consider amending the new Church law to include ministers in same-sex marriages.
