The arrest came after the suspect was barricaded in a house and surrounded by police. He surrendered about 7:45 p.m. and was expected to undergo surgery late Thursday for a gunshot wound to his neck, police said.
The suspect had been pursued there by police following the shootings of the officers, who each hospitalized in stable condition.
Earlier, while trying to elude capture, the suspect committed a carjacking in order to switch vehicles, according to authorities.
At the house, the unidentified 31-year-old suspect fired multiple shots at police, Houston police Chief Troy Finner said.
Houston's FOX 26 obtained video of the incident, where dozens of shots between police and the suspect can be heard.
In the earlier shooting, one officer was shot in a foot, another in a leg and the third in an arm, Houston Mayor Sylvester Turner said, according to reporter Jonathan Martin of FOX 26. All three wounded officers were in stable condition at Memorial Hermann Hospital, Martin reported.
In a Twitter message, Houston police identified the wounded officers N. Gadson, 35; D. Hayden, 32; and A. Alvarez, 28, all of the Northeast Patrol.
The shooting of the officers earlier Thursday had prompted a manhunt that led police to the suspect a short time later.
The incident began when police responded to a call at 2:42 p.m. about the suspect. Police located and pursued his vehicle, but after it crashed, the suspect fired multiple times, wounding the three officers.
Police fired back, but it was unknown if the suspect was hit, Finner said.
After the crash, the suspect then carjacked a Mercedes-Benz at gunpoint, and drove the vehicle to a house in Houston where he barricaded himself Thursday evening.
Police officers surrounded the house, and the suspect again fired at officers, according to Finner.
The chief disclosed during an evening news conference that the suspect had been arrested.
Mayor Turner said he and Chief Finner planned next week to map out "additional steps" for making the city safer, Martin of FOX 26 reported.
On Sunday, a Harris County constable was shot dead while conducting a traffic stop in southwest Houston.
Finner said that witnesses saw Harris County Cpl. Charles Galloway stop a vehicle when the suspect, identified as Oscar Rosales, "got out of his vehicle and immediately fired upon the deputy multiple times, striking him, and then drove off."
Last Friday night, two New York City police officers were shot while responding to a domestic violence call involving a mother and her son.
Officer Jason Rivera, 22, was pronounced dead Friday night and partner Officer Wilbert Mora, 27, died Tuesday.
Two St. Louis officers were shot in nearby Ferguson, Missouri, on Wednesday after spotting a vehicle that was possibly linked to a homicide, according to authorities.
One officer was shot in a leg while the other was shot in the abdomen around 1 p.m, St. Louis Metropolitan Police Department Chief John Hayden said.
The officer who was shot in a leg was in "very critical, very unstable" condition, the chief said.
White House press secretary Jen Psaki blamed the "underfunding" of police departments for the crime spike.
During the White House news briefing Monday, Psaki said "gun violence" was a "huge reason" for the increase in crime, and also blamed the "underfunding of some police departments and their need for additional resources."
Fox News' Houston Keene contributed to this report.