Speed is Wales' most-capped outfield player and was Wales manager from December 2010 until his death in 2011.
Former England midfielders Frank Lampard and Steven Gerrard - both Champions League winners - also make the list selected by a panel.
Ex-West Ham player and manager Billy Bonds and Arsenal goalkeeper Bob Wilson were also picked for induction.
Speed had set a record with his 536 Premier League appearances but has since been overtaken by David James, Lampard, Gareth Barry and fellow Wales international Ryan Giggs whose 632 appearances is the current record.
Sir Geoff Hurst, Gordon Banks, Sir Bobby Charlton, Peter Schmeichel, Roger Hunt, Kevin Keegan, Bryan Robson, Francis Lee, Trevor Francis, Ossie Ardiles, George Cohen, Norman Hunter, Sue Lopez and Marianne Spacey were all part of the selection committee.
Lampard began his career at West Ham and went on to make 649 Chelsea appearances before announcing his retirement in 2017.
The midfielder, Chelsea's all-time record goalscorer, won over 100 caps for England and won three Premier Leagues titles, four FA Cups as well as the 2012 Champions League.
Former Liverpool captain Gerrard helped the Reds come from 3-0 down to win the 2005 Champions League on penalties and won over 100 England caps.
Gerrard made over 700 appearances for Liverpool in all competition and was voted their greatest player in 2013.
Former Wales midfielder and manager Gary Speed has been inducted into the National Football Museum Hall Of Fame.