Los Angeles Football Club (LAFC) has announced plans to build one of the most expensive privately financed soccer-specific stadiums in the US.

Designed by L.A.-based architects Gensler, the $250m (£160m) downtown stadium is set to become the first open-air professional sports arena in the city since baseball's Dodger Stadium opened in 1962.

LAFC, which will enter Major League Soccer (MLS) as an expansion team in 2018, revealed designs for a 22,000-capacity venue on the site of the Sports Arena in South L.A.’s Exposition Park.

Gensler’s recent work includes renovating the FirstEnergy Stadium in Cleveland – home of the NFL team Cleveland Browns – and Sao Paulo's Arena Corinthians in Brazil, which hosted the opening match of the FIFA World Cup 2014.

As well as the stadium, the plans cover a 15-acre area and include a conference centre, restaurants and a soccer museum.

To make way for the new development, the ageing LA Sports Arena – opened in 1959 by then Vice President Richard Nixon – in Exposition Park will be demolished.

The project will be funded by the LAFC ownership group, which includes former basketball star Earvin “Magic” Johnson; Mandalay Entertainment CEO Peter Guber, who is co-owner of the LA Dodgers MLB team and the NBA's Golden State Warriors; self-help author Tony Robbins; and US women's FIFA World Cup winner Mia Hamm and her husband Nomar Garciaparra, a former major league baseball all-star. The 24-member group also includes businessmen Ruben Gnanalingam and the controversial Malaysian owner of Cardiff City FC, Vincent Tan.

Commenting on the project, “Magic” Johnson said: “We’re not only committed to creating a dynamic soccer experience for our fans, but are equally excited about the impact our stadium and facilities will have in reshaping and revitalising South Los Angeles.”

Soccer is popular in California – a state where 38.1 per cent of the total population is Hispanic-Latino – and the new project has the strong support of local officials who are hoping to give a much needed economic boost to the area around the arena and the surrounding communities.

“I’m excited to welcome the LAFC to the City of Angels,” said Mayor Eric Garcetti. “Los Angeles loves soccer and now the greatest sports town in America gets even better.

“I know this ownership group is committed to representing the best our city has to offer. And I’m especially pleased that this proposed stadium will be located in South Los Angeles to help revive that neighbourhood and bring more jobs and opportunity for our residents.”

South Los Angeles has poverty and unemployment rates well above the city average and the strategic plan for the construction of the new stadium will include a one-time economic activity of more than US$275m and 1,200 jobs.

Additionally, net new impacts from annual operations of the new stadium are estimated to generate more than US$129m in new economic activity, create more than 1,800 full-time jobs and produce US$2.5m in annual tax revenue.

• The LAFC stadium is one of two major stadium project planned in the region. Last month, Carson's City Council last month approved a separate plan to build a US$1.86bn (€1.68bn, £1.24bn) stadium to host two National Football League (NFL) franchises – the San Diego Chargers and Oakland Raiders.