The 31-year-old signed for Boro in the summer after leaving Southampton but, after starting 11 games at the start of the campaign, he has not been involved for two months.
After holding talks with Blackpool last week, Richardson has now agreed a deal to move to Ipswich on an initial loan.
Richardson is the fifth Boro player to leave on loan in the last 24 hours following on from the departures of Luke Williams, Adam Reach, Richie Smallwood and Andy Halliday.
One arrival that Boro are still working on is a deal for Daniel Ayala, whose loan from Norwich City ended on Thursday.
"We will be working until the last moment," said Boro manager Aitor Karanka.
"Everyone knows how important Daniel is for the team at the moment. He is Spanish, and for me, it is sometimes more comfortable for me to explain things to him first.
"He is important for the team, and the club know tht he is an important player. But we have another 24 players and the club will not be doing crazy things to keep him. Before he came, he was not playing for Norwich, and now he is playing. But we will have to see what happens."
Boro will have Rhys Williams available, as talks with Swansea have faltered over the Australian international - although Scottish champions Celtic are considering a bid.
"The club is working on a number of things," Karanka said. "Rhys is our player at the moment, and that is the only way I am thinking of things. If there is a moment when Rhys goes, then he goes.
"But until then, if he is here as my player then he will be expected to play as he has been doing in the last few games. Has there been any bids for him? No. At the moment, I only think of him and Middlesbrough."
Meanwhile, Karanka has confirmed that Chelsea loanees Nathaniel Chalobah and Kenneth Omeruo are still not ready to be included in his squad.
"They will not be in the squad because they are not ready," he said.
"Nathaniel has only been here for seven days. Kenneth has been here a little bit more but that is not really long enough to get to know my philosophy. The team is playing very well right now and they will have to wait for their opportunity."