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 were males.
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.
Officers found the suspect on the scene after having struck a total of 18 individuals. Police reported six fatalities on-arrival, the number increased to eight later in the day.
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.