Staff wanting to bring a case of unfair dismissal or discrimination now have to first notify the conciliation service Acas to see if the dispute can be resolved.
Another change sees employers facing fines if they lose a case at tribunal.
Ministers said the changes would help avoid "stress, time delays and excessive costs".
Previous government measures include the introduction last year of fees for workers looking to take their employers to tribunal.
This led to a 79% fall in the number of applications but was strongly criticised by trade unions.
Under the new rules, which have come in at the start of the 2014/15 tax year, staff or employers will be required to consult Acas before having access to a full tribunal.
Acas, which stands for Advisory, Conciliation and Arbitration Service, was set up to improve employment relations and prevent tribunals.
Another change in the law will mean that if an employer loses a case brought by an employee or former employee, and is shown to have especially poor workplace practices, it could be fined up to Â£5,000 on top of any back pay that is due to the employee.
The TUC said the fines would create a welcome new incentive for bosses to respect the rights of their staff rather than risk increased financial penalties.
The Confederation of British Industry said more work was needed to change the culture of the system of solving disputes.
Employment relations minister Jenny Willott said the Early Conciliation scheme was "good news for employees and employers".
She said: "It will help them resolve their workplace disputes, avoiding the stress, time delays and excessive costs all too often associated with tribunals."
Also coming into force in the new tax year is a rise in National Insurance allowances for employers, a fall in corporation tax to 21% and a rise in the ISA allowance to Â£5,940.
New rules aimed at reducing the number of employment tribunals have come into force.