Hodgman's signing is a major boost for Australian Rugby, eligible for the Wallabies from November 2024.
The Blues prop debuted against the Wallabies in 2020, going on to play four Tests, and is eligible for Australia through his father.
“I’m looking forward to moving over to Australia with my family and starting new with the Reds," he said in a statement
"Change is good but also comes with its challenges and that excites me.
"A new facility, new coach and a playing group that has been together for a while allows me to bring my experience and just be me.
"I’m blessed to be here and can’t wait to get started."
Meanwhile, Toomaga-Allen made his lone appearance for the All Blacks in 2013, recently making the switch to Samoa.
The 32-year-old played 115 games for the Hurricanes before heading over to Europe with Wasps and Ulster.
“I can’t wait to join the club," he added.
“I’m excited to be coming back to Super Rugby after being away for a few years and getting to know everyone at the Reds.
“I’m feeling really blessed to be able to be closer to family which is a big part of why I joined the organisation.
“When speaking to Les and Sam, we talked about the importance of family and how we as a team can keep growing as a unit on-and-off the field which was a big drawcard for me.
“I’m keen to get amongst the community in Queensland and looking forward to connecting with all the supporters around the state.”
It continues new coach Les Kiss' recruitment drive in Queensland, most recently signing Junior Wallabies prop Massimo De Lutiis along with re-signing Fijian Peni Ravai.
“We’re pleased to welcome two props of the calibre of Alex and Jeffery to our squad," Kiss said.
“Both bring experience at the highest level and will strengthen our tight-five on-and-off the field.
“There’s been a strong culture of care and connection built at Ballymore over the past few years. After talking to both Alex and Jeff, they both have a team-first mentality and will only bolster these values over the next two seasons.
"In addition, having a player of Alex’s ability qualifying for Wallaby selection in 2024 is great for Australian Rugby."