The 29-year-old was once a regular for the England senior side in all formats of the game but has been hampered by an elbow injury in recent years and has not played any Tests since the end of 2013.
However, he was invited to train with the World Cup squad in Hobart this week and will be hopeful of featuring at some point during a hectic 2015 international schedule for the England team.
Bresnan has been playing for Hobart Hurricanes in the Big Bash but will fly home over the weekend and then head to South Africa in time for the third match in a five-match series, which will take place in Potchefstroom next Saturday.
National selector James Whitaker said: ???The Lions one-day series in South Africa means we can have a group of players involved in high quality and competitive 50-over cricket in the weeks leading up to the World Cup.
“Joining the squad will give Tim the opportunity to show that he is ready to be considered if a replacement is required.”
The series starts in Bloemfontein on Sunday and Harry Gurney, Stephen Parry, Samit Patel, Jason Roy and Ben Stokes have already joined the Lions squad since their two drawn four-day matches against South Africa A.