Beckham, who trained with the Gunners in January prior to moving to France, has applied himself with distinction since joining Carlo Ancelotti's squad despite his advances years.
Arteta admits he has been inspired by the 37-year-old's longevity, though he admits it may be hard to replicate at Arsenal, given Arsene Wenger's preference for youth over experience.
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“The changes he made, in different countries and different cultures as well, that is tiring, moving your family from one side to the other.
“When people criticised him when he played for Paris St-Germain against Barcelona, I could not believe it.
“What he is doing is absolutely fantastic. He trained with us in January and to see how professional he is was unbelievable.
“I talked to him and everybody who talks about him says the same. He wants to get better and better.
“I will stay on in the game as long as my legs are good and the emotions I have every time I train and play stay intact.
“I couldn’t be cheating myself by going there and just hiding. I don’t know how long it is going to last but I started when I was 17 and so it has been a long time now.”
Arteta has started 28 league games this season – second only to Santi Cazorla (31) - and says he is happy playing his football at the Emirates.
“My family are happy here so I think I made the right choice coming [to the club] and that is not disrespectful to Everton,” he added.
“I felt it was my time to leave after what I did there and go on to a different challenge.”