The Georgia legislation is but the latest front in a wide-ranging battle over abortion rights being waged this year across Republican-controlled state legislatures in the Midwest and South. Conservative lawmakers see the realignment of the Supreme Court as presenting their best opportunity to overturn Roe v. Wade, the case that recognized a woman’s constitutional right to an abortion.

How will this new law affect Georgia?

The Georgia law, which would take effect in 2020, prohibits most abortions once doctors can discern a fetal heartbeat, a milestone that occurs before some women know they are pregnant. In practice, the limit on abortion in Georgia will now be six weeks of pregnancy, instead of 20 weeks.

Exceptions are allowed to prevent death or serious harm to the woman, and in cases of rape or incest in which a police report has been filed.

Mr. Kemp was narrowly elected last November, and the bill he signed on Tuesday was seen as crucial in maintaining the conservative support that led him into the governor’s office. Mr. Kemp and the law’s other supporters have brushed aside the risks of any political backlash.

“This is a historic day for Georgia,” Catherine Davis, an anti-abortion rights activist, said at Mr. Kemp’s signing ceremony. “This is a day that many of us who have been in the pro-life fight for years and years and years didn’t really think it would be possible, in light of the politics of the issue.”