Cameron acknowledged the contribution made by generations of hard-working immigrants, but warned Britain had for too long been regarded as a "soft touch".
Under the plans, migrants will have their unemployment benefits stopped after six months if they have no prospect of finding work and non-Europeans may face charges for healthcare.
The prime minister warned entitlement to public services was "something migrants earn, not an automatic right", adding: "We want people who are interested in what they can offer to Britain."
The speech marks the next step in a drive by Cameron's Conservative-led coalition government to bring net migration down from hundreds of thousands to tens of thousands of people per year.
But it is also widely seen as an attempt to fend off a rising challenge from the anti-immigration UK Independence Party, which pushed the Conservatives into third place in a recent by-election.
The issue of immigration has shot up the political agenda as Britain braces for a fresh influx of eastern Europeans after the European Union lifts work restrictions on Bulgarians and Romanians in 2014.
Migrants from the European Economic Area - EU countries plus Iceland, Liechtenstein and Norway - are entitled to STG71 ($A104) a week in unemployment benefits while they look for work.
But Cameron said the message this sent to new arrivals was "all wrong", insisting there must be an end to the "something for nothing culture".
Under his proposals, unemployment payments will stop after six months unless migrants can prove they have a realistic chance of finding a job, including that their English is good enough.
Cameron also targeted so-called "health tourists" who abused Britain's free-to-access NHS, insisting it was a "free National Health Service, not a free International Health Service".
For those outside the EEA, ministers will look at introducing tougher charges for treatment and a requirement to have private health insurance before receiving NHS care.
