The law -- directed at local governments -- bars the removal, renaming, removal and alteration of monuments, memorial streets, memorial buildings and architecturally significant buildings located on public property for 40 or more years.
The law creates the Committee on Alabama Monument Protection.
That body would OK waivers for modifications to the monuments, memorial buildings and streets and architecturally significant buildings on public property between 20 and 40 years old.
The committee also would consider requests for renaming of a memorial school on public property for 20 or more years. An entity that makes changes without a committee waiver would be fined $25,000 for each violation.
Schools, streets and buildings described as "memorial" are those on public property "erected for, or named or dedicated in honor of, an event, a person, a group, a moment, or military service."
Ivey's office said the aim is preserving history "for all generations to learn not only from our heroes and our greatest achievements, but to also ensure that we learn from our mistakes and our darkest hours.
"When negative aspects of history are repeated, it is often done because we have scrubbed the effects of the past from our memories. This legislation ensures that both the good and bad of our past are remembered so as to enlighten our future," a statement said.
Supporters of the law argue that it hasn't been accurate to describe the legislation as a Confederate monument bill.
The sponsor, Sen. Gerald Allen, a Republican from Tuscaloosa, and other proponents say the bill is designed to preserve all of the state's history so its citizens can learn from the past.
Allen told CNN the "comprehensive" legislation will help future generations understand "the good, bad and ugly" of Alabama history, including the civil rights era last century.
"It's a piece of legislation that protects all of Alabama history," he said. "It doesn't only touch the Confederates. It touches every facet of our state history."
Opponents -- including citizens, lawmakers and groups like the Southern Poverty Law Center
-- vehemently disagree with the law.
"This is clearly about Confederate memorials," said state Sen. Hank Sanders, a Democrat from Selma. He argues the law helps maintain the public veneration of Confederate white supremacists.
He said that "the law was not thought through" because it would affect communities that want to make sensible changes to roads and buildings.
Asked whether opponents of the legislation will fight the measure, Sanders said "we're looking into every possibility."
There has been a nationwide debate over Confederate symbols, which some argue represent slavery and injustice and others say represent history and heritage.
The issue became front and center in the United States after the 2015 massacre of nine black parishioners by a white supremacist at a Charleston, South Carolina, church.
The killer, Dylann Roof,
is seen in photos with a Confederate flag.
has recently removed Civil War-era landmarks, moves both protested and celebrated. Mayor Mitch Landrieu
defended the removal of the Confederate monuments in a speech that drew national attention.
The issue also has been contentious in Virginia and Mississippi.