Boyd, 26, told BBC Scotland that he is set to sign for former Celtic manager Strachan at the Riverside and hopes the deal will be concluded on Monday.
The player had been offered £50,000 a week to join Turkish club Kayserispor but has opted for a move to Teesside.
His signing will end speculation surrounding his next club after a successful career at Ibrox where he constantly topped the team's scoring charts.
Alex McLeish had been interested in taking him to Birmingham City and Blackburn Rovers were also reported to be keen on securing the Scotland international's signature.
But Boyd, who will move under freedom of contract, is now likely to join fellow Scots Barry Robson, Andrew Halliday and Lee Miller in the north-east of England.
And he will be familiar with ex-Celtic strikers Scott McDonald and Chris Killen, and former Dundee United midfielder Willo Flood as players Strachan has taken south since his departure from Celtic Park.
Give your reaction to Boyd's decision to join Strachan at Boro
Boyd is the Scottish Premier League's all-time top scorer, surpassing former Celtic striker Henrik Larsson's tally of 158 in December last year.
In October 2008, Boyd said he no longer wished to be selected by George Burley, the Scotland manager at the time, after being used very sparingly in international games.
But he has since returned to international football, playing for new coach Craig Levein in Scotland's 1-0 win over the Czech Republic in March.
Source: BBC Sport
Source: BBC Sport