"Thank you Los Angeles--the hard work begins but I am honored to lead this city for the next four years. Let's make this a great city again," Garcetti tweeted early Wednesday morning.
Greuel gave her formal concession speech at her campaign headquarters in Van Nuys later in the morning. She got emotional at times, saying this was a hard fought race. She asked her supporters to stand behind the city's new mayor.
"The one thing that I know about Eric Garcetti is that he cares deeply about Los Angeles and that he will work tirelessly and be a strong and innovative leader in a time, I believe, that is a critical point in the city's history," Greuel said.
In late-night speeches Tuesday, both candidates appeared optimistic and thanked their supporters for their work in the long campaigns.
"On July 1, we will assume the responsibility of creating jobs, of balancing our city's budget, of keeping our city's streets safe and improving the quality of life for all Angelenos," said Garcetti Tuesday night.
Despite record spending - more than $30 million overall - voter turnout was low. Less than 350,000 people in Los Angeles, the nation's second-most populous city, voted for mayor.
The two Democrats and City Hall regulars were in the run-off contest to succeed Mayor Antonio Villaraigosa, who will leave office July 1 after two terms.
"Eric is a true leader who I trust to guide our city into its bright future. I know I am leaving Los Angeles in good hands," said Villaraigosa. "I look forward to working with Eric and his team over the next month for a seamless transition so that we can keep Los Angeles moving in the right direction."
Meantime, voters also had to decide on four City Council seats on Tuesday. Former Assemblyman Gil Cedillo earned 52 percent of the vote to beat Jose Gardea in the runoff battle for the 1st District, which includes northeast Los Angeles, Chinatown, Pico Union and MacArthur Park.
Sen. Curren Price won 53 percent of the vote against Ana Cubas in the race for the 9th District seat representing South Los Angeles.
Mitch O'Farrell, a one-time field deputy for mayor-elect Eric Garcetti, defeated Public Works Commissioner John Choi in the battle for Garcetti's 13th District seat representing the Hollywood area.
As for the San Fernando Valley-area's 6th District, there will be a July 23 runoff between former Assemblywoman Cindy Montanez and Los Angeles Unified School District board member Nury Martinez because none of the six candidates got 50 percent of the vote needed to claim the seat outright.
City News Service contributed to this report.