Sir Alex Ferguson's comments that he expects a deal to go through for Berbatov have infuriated Spurs as has Rafael Benitez's interest in Keane.
Spurs chairman Daniel Levy singled out United boss Ferguson for criticism.
"The behaviour of both clubs has been disgraceful. We told both clubs very early on that we had no interest in selling Robbie or Dimitar, respectively, and that they should refrain from pursuing the player.
"Both clubs arrogantly chose to ignore this request and we now have evidence that both clubs have systematically been working to prise the players away from us, outside of Premier League rules of conduct."
Ferguson announced on Friday that United had made Tottenham an offer for 27-year-old Berbatov and that he was confident that the deal would go through.
Benitez admitted earlier this month that he was interested in bringing Keane, 28, to Anfield this summer.
But it was Ferguson's comments that prompted Levy to speak out about the attempts to unsettle his strikers.
"Today's public comments by Manchester United's manager, announcing that he has made an offer for Dimitar and is confident that the deal will go through with time working in their favour, is a blatant example of sheer arrogance and interference with one of our players.
"It is also probably one of the worst offences by any manager in the Premier League to date
"As a result, we have today made an official complaint to the Premier League about the conduct of Manchester United.
"Benitez made similar comments in respect of Robbie recently and we made an official complaint to the Premier League about the conduct of Liverpool earlier this week.
"I have absolutely no wish to sell either player and to date we have not accepted any offer for either."
The Premier League confirmed they had received Tottenham's official complaints in relation to breaches of the Premier League rules K3 and K8.
The next step will see the Premier League board write to all parties before deciding whether to take further action.
United issued a brief response to Tottenham's claims with a spokesman saying: "We are aware of the allegation and will co-operate with the Premier League as necessary."