The 37-year-old American has been hired as a linebacker coach for pre-season by Cardinals head coach Bruce Arians.
He said it didn't matter if a coach was "the Green Hornet" as long as players felt he or she could help them improve.
Welter, who spent 14 seasons as a professional American football player, added: "I'm honoured to be a part of this amazing team."
Arians said he had spoken to his squad about Welter and insisted "they were all very cool" with her appointment.
He added: "I thought she was the type of person that could handle this in a very positive way for women and open that door.
"It's not going to be a distraction in any way."
Welter, who has a master's degree in sports psychology, became the first female to play in a non-kicking position in a men's professional league.
She was a running back and special teams player for Indoor Football League team Texas Revolution in February 2014.
Welter also played as a linebacker for 14 seasons with the Dallas Diamonds in the Women's Football Alliance.
She was also the first woman to coach in a men's professional league after training the Revolution last season.
Welter's appointment is another significant moment for women's sport and US professional sports.
Becky Hammon, an assistant coach for the NBA's San Antonio Spurs last season, served as head coach for the team's developmental summer league team and led them to a championship earlier this month.

The 12 January fixture is the first time either side has played overseas during the regular season.
Indiana lost in the first round of the play-offs last season, while the Nuggets failed to make it out of the Western Conference.
The Toronto Raptors beat Orlando Magic 106-103 in January at the O2.
The first regular-season game to be staged in the UK was the New Jersey Nets' 116-103 success over the Raptors in March 2011.

The red sand boa is a protected species, and looks like it has two heads, because its tail is shaped like its head to help it defend itself.
The snake is prized on the black market because many believe it brings good luck or has medicinal qualities.
Police in Bangalore arrested four people trying to sell the protected creature for $1,500 (Â£1,100).
Police said plain clothes officers had organised a sting by pretending to be interested buyers.
The market for the "two-headed" red sand boas was "basically another form of cheating", PS Harsha, the local deputy commissioner of police, said.
"It is invariably used to cheat people who have some belief that it will act as good luck charm."
Sharath Babu, a wildlife warden in Bangalore's Urban district, said "it is a fallacy that it has two heads... the head and tail of the snake look alike, so if anyone tries to catch it, it strikes from the other end which is the head".
Thanks to the superstition that the red sand boa will bring its owner treasure, demand for the snake is high, with people even hiring them out for ceremonies, Mr Babu told BBC Hindi.
"It is even used for conducting rituals that would bring in rain or money. It is even believed that the heavier the snake, the more riches it will bring. So, the black market dealers shove ball bearings and other objects into the snakes. These animals die a very painful death."
Luckily for this particular snake, though, it was rescued - and has now been set free in the Bannerghatta Biological Park on the outskirts of Bangalore.
Jen Welter has become the first female coach in the NFL after being appointed by the Arizona Cardinals.
[NEXT_CONCEPT]
The Denver Nuggets will play the Indiana Pacers at London's O2 Arena in the seventh regular-season NBA game to be played in the United Kingdom.
[NEXT_CONCEPT]
India police say they have seized a rare snake, known as a "two-headed" red sand boa, from illegal smugglers.