Revenue Scotland is responsible for the administration and collection of Land and Building Transaction Tax (LBTT) and Scottish Landfill Tax (SLfT).
It collected £425m through LBTT and £147m from SLfT in the year from 1 April 2015 to 31 March 2016.
The Scottish government had originally forecast revenues of £498m in 2015-16, which was later increased to £508m.
Almost all (98%) of the 115,000 tax returns were submitted through the new online Scottish Electronic Tax System, exceeding an initial target of 90%.
Revenue Scotland's operating costs for administering the collection of taxes was £4.67m - lower than the Scottish government's original £4.81m budget allocation for the organisation.
Revenue Scotland's chairman, Dr Keith Nicholson, said the agency's first year had been "hugely successful", with the online tax system having "exceeded expectations and received widespread praise".
He added: "These achievements are a clear signal to the Scottish taxpayer that Revenue Scotland is operating efficiently and effectively as Scotland's devolved tax authority."
Welcoming the figures, Finance Secretary Derek Mackay said: "The scale of the challenge of introducing the first Scottish taxes in more than 300 years should not be underestimated, and it's encouraging to see this has been done so effectively."
LBTT and SLfT  came into effect on 1 April 2015, replacing their UK equivalents (Stamp Duty Land Tax and UK Landfill Tax respectively) in Scotland.
The revenue collected is transferred to the Scottish Consolidated Fund to support the delivery of public services in Scotland.
Revenue Scotland will also collect a Scottish replacement for Air Passenger Duty when it is introduced, but will not administer the Scottish Rate of Income Tax, which will continue to be the responsibility of HMRC.
Scotland's new tax agency has collected £572m in its first year - well above the amount that had been expected.