The Holland international is in the process of finalising the formalities of a £24 million switch to Old Trafford, having earlier in the summer announced he would not be signing a new deal with the Gunners.
Journalists understand Arsenal were prepared to make their key striker, who last season bagged 30 Premier League goals, the highest paid player in the club's history, but reluctantly agreed to sanction his departure when it became clear Van Persie wanted to move.
It is another blow to Wenger's vision of building a young squad capable of dominating Europe - having seen Cesc Fabregas and Samir Nasri also both leave last summer, while Cameroon midfielder Alex Song has been linked with a £15million switch to Barcelona.
The Arsenal manager admits Van Persie - who plundered 37 goals in all competitions in an injury-free season - will be tough to replace.
"Robin is an exceptional player in the pure sense of the term. I haven't seen many in my life who have that quality in the first touch, are so technically gifted and have that intelligence of movement in the final 20 metres," said Wenger, during a stint as a media pundit for French TV station TF1.
"Unfortunately, there is an economic reality and the desire of the player. There is no other way but to let him go.
"It is another pill to swallow, we have swallowed other ones and we have always survived, but he scored 30 goals for us in the league last season, practically one every match."
Wenger added: "The economic factor is the sole satisfying thing, but you don't play with money on the pitch, you play with the quality of the players. To lose a player of this ilk is tough."
The summer additions Olivier Giroud and Lukas Podolski will, however, go some way to offsetting the loss to the squad, as will the arrival of Spain midfielder Santi Cazorla.
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Belgian defender Thomas Vermaelen is now likely to inherit the captain's armband, and insists everyone must put the disappointment of losing Van Persie to one side as they prepare for Saturday's kick-off against Sunderland at Emirates Stadium.
Brazil full-back echoed his team-mates' comments.
Santos told ESPN: "We lost a lot. Van Persie is a high quality player, a big idol of the fans and he had a great championship season in 2011/12, but I am sure the team is much more mature.
"Today we have experienced players and also the arrival of some new players, like Santi Cazorla and Podolski, who are excellent.
"We are well focused, the team is well prepared and well motivated
"We have brought in some top quality players and I am sure that Arsenal will have a great campaign in the English league."
Alex Oxlade-Chamberlain (ankle) and Theo Walcott (thigh) will be assessed after both pulled out of England's game against Italy in Berne with injuries.