Wage growth in the UK accelerated to 3.6% in the year to May 2019, the highest rate since 2008, according to Office for National Statistics figures.
Wages have been outpacing inflation since March 2018.
A record high of 32.75 million people were in employment up to the end of May, while 1.29 million were out of work, the lowest since at least 1992.
"The labour market continues to be strong," said ONS deputy head of labour market statistics Matt Hughes.
"The number of self-employed part-timers has passed one and a half million for the first time, well over double what it was 25 years ago," he added.
"Regular pay is growing at its fastest for nearly 11 years in cash terms, and its quickest for over three years after taking account of inflation."
Why has wage growth picked up?
Two factors which started in April have helped contribute to the acceleration in wage growth.
Some NHS staff have had pay increases, while the new National Living Wage and National Minimum Wage rates have both been introduced.
The new rates benefit the lowest-paid workers in industries such as wholesaling, retailing, hotels and restaurants.
Average regular pay, before tax and other deductions, was estimated at £503 a week.
However, when adjusted for the impact of rising prices, pay is still below levels seen before the 2008 financial crisis. Average pay was £468 a week when adjusted for inflation. This is still £5 less than the pre-recession peak of £473 a week recorded for April 2008.
How do men and women's employment rates compare?
The unemployment rate remained at 3.8% as expected, its joint-lowest since the three months to January 1975.
But the growth in employment slowed to 28,000, the weakest increase since the three months to August last year.
The employment rate for men was 80.2%, slightly higher than a year earlier, while the rate for women was 72%, the joint highest since records began in 1971.
Vacancies fell to their lowest level in more than a year of 827,000 across the UK - 9,000 fewer than a year earlier and 19,000 fewer than the previous quarter.
Some recent surveys of companies have suggested employers are becoming more cautious about hiring in the lead-up to the new Brexit deadline of 31 October.
How have the experts reacted?
"Despite signs that employment growth is tailing off, the labour market remains tight, with the unemployment rate at a multi-decade low," said Alpesh Paleja, principal economist of lobby group the CBI.
"It's encouraging that pay growth has picked up further, putting more money in people's pockets, but as recent data shows productivity remains in the doldrums."
Ian Stewart, chief economist at Deloitte, said: "The jobs market seems to have defied gravity, with wages rising and unemployment falling even as growth has slowed.
"The big question is how long can that last. With job vacancies edging lower and firms more cautious on hiring, the pace of job creation could slow from here."