The measures were ordered after Lohan angered Superior Court Judge Marsha Revel by failing to show up for a hearing last week in Beverly Hills and instead attended the Cannes Film Festival in France.
Photos from Cannes showed the actress partying on a yacht into the late hours on the day she was supposed to be in court in Beverly Hills.
A bench warrant was issued for her arrest then lifted when her lawyer posted bail and Lohan flew back to the United States over the weekend.
Lohan's lawyer said the actress had her passport stolen in Canne and couldn't travel in time to attend the hearing.
Lohan, wearing a dark gray pants suit, arrived in court a few minutes late and appeared somber and concerned when she conferred with her attorney about the move to attach the bracelet and require drug and alcohol testing every week in the Los Angeles area.
The bracelet gets a signal through the skin if a person has been drinking and sends the signal to the company that monitors it, court spokesman Alan Parachini said.
Lohan should be familiar with the alcohol detection device. She was seen wearing one when she left the Promises rehab center in Malibu in 2007. She posed for a promotional picture that year wearing a bikini, the ankle bracelet and spike heels.
Lohan's attorney, Shawn Chapman Holley, told Judge Revel that Lohan was planning to travel to Texas to film a movie titled "Machete."
Revel suggested the actress might have to delay the project and was unmoved when Holley suggested Lohan could fulfill the probation requirements in Texas.
Revel stressed that she was prepared to spend a half-hour reading Lohan and Holley a list of her reasons for ordering the bracelet, drug tests and an alcohol-education program.
Holley conferred with Lohan then accepted the judge's decision. Asked if she understood the orders, Lohan said quietly, "Yes, your honor." It was her only statement in court.
Holley noted that Lohan had missed one previous hearing after he uncle died.
"Did she attend the funeral?" the judge asked coldly. Holley turned to Lohan, who sadly shook her head no.
Lohan, 23, did not address a throng of media outside the courthouse before joining Holley at the hearing. The actress rushed past the media on her way out, leaving in a waiting SUV.
The actress has been on probation since August 2007 after pleading guilty to misdemeanor drug charges and no contest to three driving charges.
Revel set a probation violation hearing for July 6 to address Lohan's failure to appear in court last week for a scheduled progress report on the probation stemming from the two high-profile arrests.
Lohan, who gained fame in the movies, "Mean Girls" and "The Parent Trap," has provided the tabloid media with lots of fodder with her personal escapades. She spent more than two hours after the hearing waiting for a bracelet to be placed on her ankle. Lohan must wear the bracelet until the July hearing, when the judge will decide if it will remain in place, Parachini said.
Lohan was to be arrested upon her return to Los Angeles for missing the mandatory hearing, but the judge recalled the warrant late Thursday after Lohan posted bail.
Holley said Lohan's passport was stolen and she had proof Lohan had an airplane ticket to return for that hearing.