The increase was partly driven by more people coming to the country last year than those who left.
There were also 56,014 births registered, which was more than the 54,700 deaths recorded during the same period.
Official statistics from the National Records of Scotland show that although 75,900 people came to Scotland from the rest of the UK and overseas and 65,900 left, the net gain of 10,000 was lower than previous years.
Despite the estimated population being at a record high, there were 2,013 fewer births than 2012 but also 0.4% fewer deaths.
By June 30 last year, there were 2.4 million households in Scotland, which is an increase of around 171,000 over the past 10 years.
In other figures published today, it was revealed there were 27,547 marriages in 2013.
The average age at which people marry for the first time has increased by around two years since 2003 to 33 for men and 31.2 years for women, the figures also show.