The law was essentially designed to challenge a 1973 US Supreme Court decision, known as Roe vs. Wade, that made it legal for women across the nation to have an abortion.
Governor Mike Rounds, a member of President George W. Bush's Republican Party, acknowledged as much in his remarks on signing the legislation.
"Because this new law is a direct challenge to the Roe versus Wade interpretation of the Constitution, I expect this law will be taken to court and prevented from going into effect this July," he said.
Rounds said it would likely take years for the law to end up in the supreme court, but that the court would have an "opportunity to reconsider an earlier opinion".
The challenge to the 1973 decision came only weeks after the second of Bush's Supreme Court picks was sworn into office. New Chief Justice John Roberts and Associate Justice Samuel Alito are believed to be conservatives, and abortion opponents hope they could cast the decisive votes in overturning Roe vs. Wade.
The South Dakota law outlaws most abortions in the state, except if the mother's life is at risk. Doctors performing an abortion in other circumstances could risk a prison term of five years.
Nancy Keenan, head of the US abortion rights group NARAL Pro- Choice America, has called the measure "dangerous and unconstitutional".
The South Dakota law is seen as the most serious attempt to challenge Roe vs. Wade since a 1989 Supreme Court ruling upholding the right to an abortion.