Smith has been under pressure and Villa have dismissed the 50-year-old following Friday night’s 1-0 defeat at Southampton.
Villa’s poor run leaves them 15th, just three points above the relegation zone.
Smith leavesafter three years in charge and is the fifth managerial change in the Premier League this season.
Villa chief executive Christian Purslow said: “When Dean joined us in October 2018 our team was really struggling in The Championship. He immediately transformed the atmosphere and performances and achieved the ultimate success of leading Villa back to the Premier League within the same season – a rare feat.
“He then secured our place in the Premier League after a tough campaign and took us to a Cup Final at Wembley.
“However, after a good start to last season, this year we have not seen the continuous improvement in results, performances and league position which we have all been looking for. For this reason we have decided to make a change now to allow time for a new head coach to make an impact.
“The board would like to sincerely thank Dean for his many excellent achievements, on and off the pitch, during this time. Everyone knows how much Aston Villa means to Dean and his family. He has represented the club with distinction and dignity – universally liked and respected by everybody associated with Aston Villa – our staff, players and supporters alike. We wish him the very best.”