Scott said he is still "not persuaded" about the guardian program under which participating districts can authorize staff members to carry handguns if they complete law enforcement training.
"I'm glad however, the plan in this bill is not mandatory", he said, adding that the program will be up to local officials to implement.
State Rep. Jared Moskowitz - a Democrat who represents the South Florida district where the shooting happened - said in a text that Scott will sign the bill on Friday.
The proposal (SB 7026) would raise the minimum age from 18 to 21 and require a three-day waiting period for people purchasing rifles and other long guns, requirements that already apply to buying handguns.
"If counties don't want to do this, they can simply say no", he said.
The governor singled out two fathers, Pollack and Ryan Petty, who both made repeated trips to Tallahassee to lobby for the legislation.
"I know the debate on all these issues will continue".
Surrounded by families of those who died in the attack, Scott said he was signing the measures into law because "this is a time for us to come together, roll up our sleeves and get it done".
Student activists from the school where the shooting took place, called it "a baby step". It should have been obvious that we needed to do something after Parkland.
"Marjory Stoneman Douglas High School is being shot up", the caller said before the call ended in a dial tone.
"We have paid a bad price for this progress", said Tony Montalto, a Parkland parent whose daughter Gina was one of the murder victims.
The National Rifle Association has sued Florida after it passed a gun control law in the wake of a school shooting last month that left 17 people dead.
"Our teachers and other school employees are ready to fiercely defend our students but none of them should ever have to choose between shepherding students to safety or confronting an armed assailant where they are sure to draw fire towards the very students they are trying to protect", Joanne McCall, president of the teachers' union, wrote in a letter to the governor.
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Scott told the students: "You helped change our state. You should be proud".
The Florida Education Association on Thursday asked Scott to veto the measure, saying more than 200,000 school employees could qualify to carry firearms, which would "do more harm than good". In a statement Thursday, NRA and Unified Sportsmen of Florida lobbyist Marion Hammer called the bill "a display of bullying and coercion" that would violate Second Amendment rights and punish law-abiding citizens.
In schools, the measure also creates new mental health programs and establishes an anonymous tip line for reporting threats. The program's language specifically excludes most teachers, except in the case of Junior Reserve Officers' Training Corps educators and teachers in the military or law enforcement.
Marjory Stoneman Douglas High School student David Hogg has been an outspoken advocate for stricter gun laws since a teenager with an AR-15 killed 17 people at his school.
Lawyers for the NRA want a federal judge to block the new age restriction from taking effect.
A statewide association of Florida school superintendents called on Scott to veto the $67 million for the guardian program. The governor can not veto individual items in the bill itself, but he does have line-item veto power with the budget.
The complaint says the law violates the second amendment of the United States constitution, which governs the right to bear arms.
But he again expressed some reservations about arming school staff.
The Republican governor, who is expected to seek a U.S. Senate seat later this year, has called for raising the minimum age to purchase any type of gun and said he does not support arming teachers.
Cruz, now 19, had a history of mental issues, numerous encounters with police and was expelled from Stoneman Douglas previous year for disciplinary problems, according to authorities.
Meanwhile, the 19-year-old former student accused of opening fire at the school on February 14 made his initial appearance before a judge on 17 attempted murder charges added this week by the grand jury.
Cruz's public defender withdrew an initial not guilty plea, leaving him to "stand mute" for now, but has said he will plead guilty if prosecutors take the death penalty off the table and sentence him to life in prison instead.