Financial terms of the transaction were not released.
"I am thrilled to have H-E-B join forces with another well-respected and innovative Texas company", said Martin Otto, H-E-B's chief operating officer.
H-E-B representatives told the Statesman that consumers won't initially see the grocery chain pushing Favor's services in its 400 stores, but H-E-B does plan to grow Favor along with themselves.
Jag Bath, who was hired as CEO in September 2015, will remain in his position and H-E-B says it is keeping all of Favor's 50,000 runners.
Favor operates in more than 50 Texas cities and suburbs, including much of Tarrant County.
The supermarket retailer is buying Favor Delivery, an on-demand delivery service headquartered in Austin, Texas.
Already the grocer with the largest footprint - by far - in Texas, H-E-B is making a big bet on digital as it looks to ensure a future filled with continued growth.
"Over the past two years, we have established a strong working relationship with Favor that has proven to be immensely successful for both companies", Otto said. This year, the company - which employs more than 106,000 people between both countries - will celebrate its 113th anniversary.
H-E-B acquired the Austin-based Favor Delivery, which distributes restaurant meals and groceries via a mobile app.
Curbside pickup is also offered at more than 100 stores, and through H-E-B's website customers can order and ship grocery, drugstore, and general merchandise products to 48 states and military bases worldwide.
Grocers have been scrambling to improve delivery services after Amazon.com's acquisition of Whole Foods Market.