Legal Affairs minister Roseanna Cunningham said concerns had previously been expressed that the current arrangements were "extremely complex and fragmented".
She added that a review had found many tribunals were not sufficiently independent of the Scottish Government and lacked a consistent system of appointment for chairs and members.
But she said legislation from the Scottish Government, which was unanimously agreed at Holyrood, would tackle these issues.
Ms Cunningham said: "The Tribunals Bill addresses these concerns by simplifying the structure, guaranteeing independence and introducing a uniform appointment system for members."
The Scottish Government plans to establish two generic tribunals - a First-Tier Tribunal to hear initial cases and Upper Tribunal Scotland, which will mainly deal with appeals from the first tier.
The Bill proposes bringing tribunal judges under the leadership of Scotland's top judge, the Lord President of the Court of Session.
An office of the president of Scottish tribunals is to be established, which will be responsible for ensuring business runs effectively and efficiently.
Under the plans, existing tribunals will be phased into the new First-Tier Tribunal one by one.
Labour backed the changes, with Elaine Murray stating these mirrored legislation already in place south of the Border.
She added: "We agree that the tribunal system in Scotland is a very important part of the justice system."