His second Budget on 8 July will outline policies to tackle tax avoidance and aggressive tax planning by the rich, as well as detail plans on welfare spending, Osborne announced in a letter in The Sun.
Osborne said his new Budget would be written with "working people" in mind and aim to "entrench stability and security".
The big announcement in the March Budget related to the cut in the pensions lifetime allowance - from £1.25m to £1m, a move which concerned many advisers and other stakeholders, including new pensions minister Ros Altmann.
Among the Conservative promises in the party's pre-election manifesto were that the personal allowance would rise to £12,500, with the 40% threshold for higher rate income tax payers jumping to £50,000. There was also a promise not to increase income tax, NICs or VAT before 2020.
For pensioners, the Tories said they would restrict tax relief on pension contributions for those earning £150,000 and above, and maintain the 'triple-lock'.
Elsewhere, they said ISAs would be inheritable by a spouse or civil partner and that there would be a £175,000 per person transferable allowance for partners when their main residence is passed to children on death.
Although Osborne did not touch upon all the Conservatives' election promises in his letter, he said tax avoidance would be high on the government's agenda.
Writing in The Sun, Osborne commented: "We will protect the NHS and give it more funding each and every year, while making savings across Whitehall.
"We'll crack down hard on tax avoidance and aggressive tax planning by the rich - because everyone should pay their fair share.
"We will always protect the most vulnerable, but we also need a welfare system that's fair to the people who pay for it. If you can work you should be working, so we'll take the next steps in our benefit reforms to make sure that happens.
"Second, we've got to go on helping businesses create jobs in Britain, so we move towards full employment. That means facing a hard truth: in Britain we produce about a quarter less for every hour we work than countries like America or Germany. Fixing that long-running productivity weakness is the big challenge for the next five years.
"So in the Budget we'll spend less on welfare, and instead invest to create three million more apprenticeships, so that young people can learn a trade, get better jobs and earn more."