Michael Engel, a 31-year-old yacht engineer living in Cornwall, said he and wife Natalie plan to go back to South Africa with 18-month-old daughter.
A Home Office spokesman said the rules were designed to stop foreign spouses becoming reliant on British taxpayers.
The couple were told of the immigration tribunal's ruling after they had appealed on the grounds of a right to family life, the BBC reported.
Mrs Engel's craft-making business made 19,786 pounds in 2014 which was deemed not enough by the tribunal panel, which met on December 3.
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She said the decision made her feel like her family was being "kicked out" of the country.
She said: "I'm gob-smacked, lost for words, angry and deflated. I'm not so proud to be British right now."
The couple are now awaiting a deportation date. They met in 2009 working on a cruise ship and lived in South Africa for four years.
They moved to the UK in January 2013 with Engel on a holiday visa, living first in Yorkshire and then in Cornwall.
In a statement the Home Office said: "Our family rules were brought in to make sure that spouses coming to the UK do not become reliant on the taxpayer for financial support.
Average gross full time pay in Cornwall was 23,305 pounds for the year ending April 2014, compared with 27,195 pounds for the UK, according to the Office for National Statistics.