Alvarez has been charged with eight counts of manslaughter and 10 counts of aggravated assault with a deadly weapon, Brownsville police announced Monday.
Officials say all the victims are males, several of whom are from Venezuela.
Officers found the suspect on the scene after having struck a total of 18 people. Police reported six fatalities on arrival, and the number increased to eight later in the day.
“Through the investigation, it was found that the SUV ran a red light, lost control, flipped on its side and struck a total of 18 individuals,” Chief Felix Sauceda said at a press conference.
The investigation also found that Alvarez “attempted to flee the scene after impact, but was held down by several individuals on scene,” Sauceda said.
Alvarez is a Brownsville resident with a lengthy criminal record, including charges of driving while intoxicated, aggravated assault and assault against the elderly or disabled, police said.
The group was waiting for a bus outside a migrant center Sunday in the border city of Brownsville, Texas. At least 10 others were injured, authorities say.
With no bench at the unmarked city bus stop, some of the victims were sitting on the curb around 8:30 a.m. when the driver hit them, surveillance video from the Bishop Enrique San Pedro Ozanam Center showed.
Alvarez is being held on a $3.6 million bond.