Bingham, 22, who had a loan spell with Falkirk in 2013, spent the last season with Hartlepool United.
The 29-year-old Seaborne rejected a new contract with Partick Thistle after two seasons at Firhill.
Accies manager Martin Canning said: "We're just waiting for the clearance to be confirmed for both of them."
Seaborne, who joined Thistle after leaving Coventry City in 2014, made 35 appearances for Accies' Premiership rivals last season.
Bingham, who began his career with Wigan Athletic and had a spell with Mansfield Town, scored four times in 38 appearances for League Two outfit Hartlepool last season.
"In Dan, I have been looking for a bit more experience and he brings that to the team," Canning told BBC Scotland after Friday's 1-1 draw with Dundee.
"The two guys who played tonight played well and it gives us good competition now.
"Up top, we've got Rakish coming in who offers something slightly different to Alex D'Acol, Eamonn Brophy and Shaka Roy, who are stronger, take the ball in.
"Rakish can also take it in, but he gives you that threat in behind. He's quicker and more mobile, so hopefully that gives us a better balance up top as well."
The point at Dens Park leaves Accies third bottom of the table with two points from their opening three games and having played one more game than Hearts and Inverness Caledonian Thistle.
However, Canning stressed: "We are in a good place.
"Our squad's strong I feel and I have been trying to bring in a couple - and the right people - and it's taken a while to get those deals done."
Hamilton Academical are in the process of completing the signings of defender Danny Seaborne and striker and fellow Englishman Rakish Bingham.