The Professional Game Match Officials Limited (PGMOL) confirmed the appointment on Thursday and also said Sam Allison would become the first Black official to take charge of a Premier match for 15 years.
Allison will be the referee for Sheffield United v Luton Town on December 26th.
Howard Webb, the PGMOL's head of referees, said both Welch and Allison deserved their chance.
"They are both part of the PGMOL development group which fast-tracks talented officials through the pathway," Webb told Sky Sports. "We have already seen three officials from the group take charge of their first Premier League games and now we have number four and five and it shows the value of that work.
"We have not seen a female take charge of a Premier League game before so it's significant, and Sam being the first Black official with a whistle in the Premier League since Uriah Rennie. It demonstrates people can make it through the pathway from groups that are not traditionally well represented."
Welch has been a trailblazer for female referees and last month was the fourth official for Fulham v Manchester United in the Premier League, the first female to fulfil that role.
The 40-year-old, a regular in the Women's Super League, has previously officiated in the Football League and the FA Cup and was on duty at the women's World Cup this year.
The PGMOL has made greater diversity one of its aims and Allison will become the first Black referee in the Premier League since Rennie retired in 2009.
Allison, a former firefighter, was promoted to the Football League in 2020 and moved up to the second-tier Championship earlier this year. No Black or Asian referee has taken charge of a Premier League game since Rennie's last match in 2008.
