Eric Simms was born in Karuah, New South Wales on 2 August 1945, the eldest son John (Jack) Simms, a Ullugundy Island man, who came to Karuah to live for a while before moving to La Perouse in Sydney. His mother was born Gwendoline May Cook and became Gwendoline Ping when her mother remarried. He and his sister, Beverley, grew up on the former Aboriginal Reserve at Karuah, raised by his mother and stepfather, Fred Ridgeway, and with six other younger brothers and sisters.

Simms moved to La Perouse where he played for La Perouse Panthers Junior Rugby League Football Club in the 1964 premiership-winning team. He was a 19-year-old truck driver when he was signed for South Sydney in 1965. He played in the centres for South's grand finalist team which lost to St George (12 – 8) before a then record crowd of 78,056; Simms scored the last points in the game with a penalty goal.

In the 1968 Rugby League World Cup, Simms gained the distinction of becoming the fourth Aboriginal to represent Australia in rugby league. He scored 50 points in four games at the 1968 World Cup, a record which still stands today.

Simms went on to play 206 first grade games, scoring a total of 1,841 career points. In 1969, he broke the record for the most points scored in a premiership season with 265, previously held by Dave Brown of Eastern Suburbs. He held the record until broken by Mick Cronin over a decade later.

He played in the 1970 World Cup in England two years later and scored 37 points in total. The final, played at Leeds in November, 1970 has been described "as the most Savage international ever played" and "a running brawl"; after the full-time whistle, with Australia having won, Simms offered a handshake to the English winger, John Atkinson, who responded by head-butting Simms.

In 1973 he overtook Keith Barnes' record for the most points scored in an NSWRFL career (1,519); Simms' eventual total of 1,841 stood as the new career record for ten seasons until it was bettered by Graham Eadie in 1983.

After the 1975 season, Simms moved to Crookwell, New South Wales, with his wife Sue and three children, Brendon, Kristie and Simone where he was captain-coach in 1976 until an arm injury (sustained in a tackle) forced his playing retirement at age 31. He coached Crookwell in 1977 and returned to Sydney where he coached the La Perouse team in 1978.

In 1977, Simms returned to the family home, Chifley Sydney where he started work on the wharves, an industry in which he has worked for more than 30 years. He worked at Port Botany where the demands of shift work put an end to his coaching days and his rugby league career. By 1997, he was a foreman for P&O on the White Bay wharves at Port Sydney. In September, 2008 he was living in a southern Sydney suburb and working at the Rozelle wharves.

In 2001 he was named in the Indigenous Team of the Century at the Eric Simms Challenge - A Tribute to Indigenous Rugby League, Redfern Oval, June 2001. The team was chosen by a panel chaired by then Senator Aden Ridgeway, a former South Sydney junior league player and then deputy leader of the Australian Democrats in the Australian Senate; other panel members were Ian Heads (rugby league Journalist and historian), Frank Hyde, Roy Masters and David Middleton (a rugby league historian). The Eric Simms Challenge was described by the Rabbitohs' marketing manager as "a salute to all Aboriginal and Torres Strait Island players, past and present" and was a match between the NRL Rabbitohs team and a representative Aboriginal team, the Murdi Paaki Warriors, a development side from western New South Wales ("from the Queensland border, across to Burren Junction in the east, to Gulargambone in the south-east, through to Bourke, Cobar, Ivanhoe and down to the Victorian border").

In August 2008, Simms was named at fullback in the Indigenous Team of the Century. Simms set several records in his playing days, some which still stand. He is also noted for his goal-kicking ability (field, penalty and conversion): he once kicked five field goals in eleven minutes (against Penrith in 1969). It has been said of Simms and his ability to kick field goals that he is "one of the few men whose influence was such it singlehandedly changed the game."