Five ministers were replaced, including Defence Minister Naoki Tanaka. Satoshi Morimoto, an academic, succeeds him.
The opposition Liberal Democratic Party had wanted four ministers removed.
Mr Noda's government wants to double the consumption tax rate to at least 10% by 2015 to help cut Japan's public debt and fund rising welfare costs.
"This reshuffle is to strengthen the cabinet and ensure that the government can make progress on several different policies, including tax and welfare reform," the prime minister told a news conference.
"I cannot allow this bill to be defeated. I will do my best to make sure this bill gets passed."
Mr Morimoto, a well-known security policy expert at Takushoku University, is reportedly the first non-politician to serve as Japan's defence minister.
Apart from Mr Tanaka, the Liberal Democratic Party had also demanded the removal of the ministers of transport, justice and agriculture, who face allegations of misbehaviour.
Mr Noda also replaced the minister for financial and postal reform.
The consumption tax legislation still faces challenges in the opposition-controlled upper house and from within the ruling Democratic Party.
The cabinet approved an outline of the legislation in February but has been stuck in negotiations since.
Mr Noda is looking to present the bill to the lower house before parliament ends its session on 21 June.
Japan's Prime Minister, Yoshihiko Noda, has reshuffled his cabinet in an effort to gain opposition support for a bill that would double sales tax.