Taking to Twitter on Wednesday, Ms Truss wrote: “Excellent news that CPTPP nations have agreed UK accession process will commence to join this dynamic free trade area of 11 countries.
“We’ll present our plans to Parliament in the coming weeks before starting negotiations.”
In response to Ms Truss’ comments, Mr Rees-Mogg tweeted: “Free trade is always the key to prosperity.”
The CPTPP removes barriers such as quotas and tariffs but, unlike the EU, it does not aim to create a single marker or a customs union or create wider political integration.
Ms Truss has refused calls from opposition MPs to provide an economic assessment of the benefits of the UK joining the Asia-Pacific agreement.
The process of Britain joining the CPTPP starts with the forming of a working party to assess the UK’s compatibility with the trade deal.
The UK said it would work with Japan, who are chairing the group this year, to conduct talks as quickly as possible.
Last October, the UK negotiated its first major post-Brexit trade deal with Japan.