Ann graduated from Highland Park High School in University Park, Texas, where she was a childhood friend and high school classmate of Jayne Mansfield. After graduating from the University of Texas in 1957, Wedgeworth moved to New York, where, after several auditions, she was admitted to The Actors Studio.
Wedgeworth joined the cast of Three's Company in 1979. After the departure of Mr. and Mrs. Roper, Wedgeworth somewhat replaced Mrs. Roper's love-starved personality as Lana Shields, an older neighbor who has had three previous husbands. Lana first appears in "Love Thy Neighbor" (season 4, episode 2), when Jack Tripper is talked into being Lana's date. "Mrs. Shields", as Jack originally addresses her, becomes head-over-heels in love with him, and by the end of the episode has moved in next door to Jack, Janet Wood, and Chrissy Snow. However, after a few episodes Lana's appearances became smaller and less frequent. Lana disappeared from the show before mid-season, with no explanation given.
It is in the episode "A Black Letter Day" (season 4, episode 13) that we see the last of Lana, as per the episode description, "Lana thinks Jack is having an affair with Janet or Chrissy after she reads an advice column and jumps to conclusions". In one of the episode's last scenes, Lana angrily dumps a drink on Jack's head, and storms out of The Regal Beagle. After this, we never see or hear of Lana again.
Wedgeworth revealed to author Chris Mann that she wasn't "fired", but rather asked to be let go. After shooting a couple of Three's Company episodes, Wedgeworth said that some of the cast members were complaining about the size of her role, and subsequently, her part dwindled down to "practically nothing". Wedgeworth asked the producers to re-write the part of Lana back to the way it was intended and promised to be, or release her so that she could pursue other opportunities. The producers thereupon released her from the show.
In 1982, Ann worked with Linda Bloodworth-Thomason in her first series, the short-lived CBS-TV series Filthy Rich, playing ditsy, good-natured Bootsie Westchester. In 1986, she had a memorable role as a nasty toy store saleswoman in an episode of The Twilight Zone. In 1990, she had a walk-on role on ABC-TV's Roseanne where she played Dan Conner's mother.
Throughout the 1980s, Wedgworth took many supporting roles in films such as Killjoy (1981) and No Small Affair, playing Jon Cryer's mother in the latter film. In 1985, Wedgeworth appeared in the TV movie Right to Kill?. In 1987 she appeared as a mother who is unknowingly reunited with her dead son in Made in Heaven, and she appeared in A Tiger's Tale that same year. In 1989 she portrayed Aunt Fern in the box office hit Steel Magnolias, directed by her friend Herbert Ross, who also directed her in her Tony-winning role in Chapter Two. She also appeared in the 1991 film Hard Promises.
From 1990 to 1994 she played Merleen Eldridge on the CBS sitcom Evening Shade.
Most recently, Wedgeworth was seen in The Hawk Is Dying, with Paul Giamatti, shown at the Sundance Film Festival.
She married actor Rip Torn in 1955. They have a daughter, actress Danae Torn. The couple divorced in 1961. In 1970 she married acting teacher and director Ernie Martin, and they have a daughter, actress/acting teacher/writer Dianna Martin.