Meanwhile, the number of people coming north to Scotland his risen by almost a tenth since 2011, the Office for National Statistics has said.
Economic factors and the impact of university tuition fees, which has made it "more financially favourable for students to remain in Scotland", is likely to have contributed to a decline in Scots moving south, according to the ONS.
It is unknown whether the independence referendum - which was announced in 2011 - has had any effect, statisticians said.
Some 37,741 people left Scotland to go to England and Wales in 2013, 6% fewer than 2012 and a fifth lower than 2002.
Meanwhile, the number of people coming to Scotland has risen steadily from 41,333 in 2011 to 45,012 in 2013, although this is almost a sixth lower than 2002 and down from a peak of 60,090 in 2004.
The ONS said: "The overall number of cross-border moves has been lower in recent years than it was earlier in the series.
"The number of moves into England and Wales from Northern Ireland has varied comparably little, but there have been declines in the number of moves to Northern Ireland, as well as the number of moves both into and out of Scotland (since 2002).
"As with moves within England and Wales, it is likely that economic factors have had an impact on cross-border flows.
"Another factor likely to have had an effect is the differing, and evolving, policies on university tuition fees in the different parts of the UK, in particular that it has become financially more favourable for students from Scotland to remain in Scotland for study.
"It is not known whether the forthcoming referendum on Scottish independence, and the associated debate, has had any effect."