The former London Irish head coach joined the England set up in 2008 and was the only member of the frontline coaching staff to have been appointed by team manager Johnson himself.
Smith has opted against firing a parting shot at his critics upon his departure and has instead given a simple reminder of England's results prior to their World Cup exit to France.
"Although the World Cup was a massive disappointment, we have won 10 out of the last 13 games," said Smith, who played international rugby for Australia and Ireland.
"Johnno appointed me and gave me the opportunity, and that's something I will be forever grateful for.
"He has been fantastic to work for and has always given 100 per cent and maintained the utmost integrity. Working with the other coaches has also been a positive experience and I wish them all well."
And while reports suggest Smith wasn't too highly rated by some of his players, Johnson feels the 45-year-old deserves great credit for his achievements during his three years at Twickenham.
"If you look at our record in the last 12 months, and the fact that we have scored 37 tries to 12 conceded, it shows what an impact Brian has made," said Johnson.
"Brian has brought a high level of coaching and a huge amount of commitment and passion to the job.
"I want to thank him for what he has done for the England team and for the young players that he has brought on."
Forwards coach John Wells, defence coach Mike Ford and scrum coach Graham Rowntree are currently still in position but their futures remain unclear as the Rugby Football Union looks towards Johnson's replacement.