The freeze will cost £640m over four years, less than the £1.9bn over five years cost projected by Transport for London during the election campaign.
Mr Khan will review TfL's layers of management, cut agency staff, review projects and freeze salaries of top managers to make savings.
Travelcards, monthly Oyster cards and daily caps are exempt from the freeze.
The Liberal Democrats have criticised the mayor for breaking his fares freeze promise as the benefits will not be felt by passengers using travelcards.
"Not what he said in his campaign," said Lib Dem London Assembly Member Caroline Pidgeon.
Conservative group leader Gareth Bacon said: "Sadiq Khan was asked about his fares freeze thousands of times during the mayoral campaign.
"Not once did he mention that this freeze would not include travelcards."
Mr Khan said he could only freeze TfL fares, not those under the control of Department for Transport.
"Londoners currently pay some of the highest public transport fares anywhere in the world," the mayor said.
"My fares freeze on TfL services will make life easier for millions of people and will ensure that London becomes a more affordable city for all."
London's transport commissioner, Mike Brown, said the savings needed to deliver a fares freeze for two years had been found, and the rest of the money could be found in the autumn.
"For the first two years it is enshrined. The money is there.
"Over the summer... all the money will be found. We will achieve this."
The new mayor will:

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Conor Kernohan put the holders ahead with a close-range header from Stuart Nelson's cross in the second half.
But Matty Doherty quickly levelled for the Derry side with a penalty after Grosvenor keeper Tim Larmour had brought down Joe McCartie.
In extra-time Josh Kelly rounded keeper Gareth Muldoon to make it 2-1 and skipper Nelson's low shot sealed it.
Nelson, who also played in Grosvenor's 2016 triumph, praised the effort of losing finalists St Columb's.
"They are a quality side and, as you could see today, they stroke the ball about nicely," said the winning captain.
"I thought our fitness maybe told in the end, although we got lucky with two breakaway goals.
"We had to dig deep, but the boys have been brilliant all year."

Prime Minister David Cameron said last week that money was "no object" in the effort to aid households and businesses flooded in England in recent weeks.
Parts of Dumfries and Galloway were hit by flooding over the festive period.
Councillor Colin Smyth has called on Scottish ministers to ensure the region gets a share of any additional cash.
He said: "What we are asking is, if there is funding being made available in the south of England will Scotland receive some of that as part of the Barnett formula?
"And secondly we want to know from the Scottish government, if this is the case, will they make sure that money is spent in the areas that actually suffered from flooding."
Dumfries and Galloway was one of the Scottish areas hardest hit by flooding at the end of last year and over the new year period, with residents of Kirkconnel, Carsphairn and Moniaive having to be evacuated.
One family was rescued by helicopter after their farm house beside the River Nith near Closeburn was cut off by rising water.
Just days later, coastal communities along the Solway bore the brunt of more severe flooding as high tides, storm surges and gale force winds combined to overwhelm sea defences.
In January, Scotland's Environment Minister Paul Wheelhouse said flood risk management was a "priority".
He said Cosla and the Scottish government had a "pot" of Â£42m available to local authorities to bid for to help tackling flooding issues.
Most passengers will pay the same fares in 2020 as they do now, London Mayor Sadiq Khan has announced.
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Grosvenor retained the Schools' Cup by beating St Columb's 3-1 after extra-time in the final at Seaview.
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Dumfries and Galloway Council has said flood victims in the area should receive a share of UK government money to help those hit by severe weather.