Smith, who helped guide his country to World Cup victory at home last year, told the Rugby Football Union website that he had decided to stay in New Zealand for personal reasons.
"It was an incredibly difficult decision," he said, after ringing England head coach Stuart Lancaster to tell him his decision.
"I took the job with the (Waikato) Chiefs so I could move nearer to elderly parents. I have travelled the globe with rugby for the last 15 years and I want to fulfil my commitment to be closer to them.
"I do also feel some loyalty to the Chiefs and the job that I have with them and leaving after eight months when I have a year left on my contract did not feel right."
Former England utility back Catt will leave London Irish after Saturday's final Premiership game against Gloucester for England duties from May 7 to June 30.
"Mike has played at the top level and is highly respected. He has done a great job whilst coaching at London Irish and we are looking forward to working with him on this South Africa tour," said Lancaster in a statement.
"He is experienced in playing in South Africa and this will be invaluable as we prepare for this challenging and exciting tour."
South African-born Catt, a World Cup winner who retired from international rugby in 2007, has been with London Irish since 2004.
England open their tour of South Africa in Durban on June 9 with the first of three tests.
The second test will be played in Johannesburg on June 16 after a midweek match against the South Africa Barbarians South in Kimberley on June 13. They then play South Africa Barbarians North in Potchefstroom on June 19.
The final test is in Port Elizabeth, Catt's birthplace, on June 23.