Moving here does not mean moving to a new city or something like that. I am talking about the people that just can't stay at one place. It is impossible for them to sit put at one place and relax.
If you're talking about a person who's unable to sit still (as opposed to having an irresistible urge to travel), the word we used when I was growing up was hyper, short for hyperactive. Nowadays the full name of the diagnosis is Attention Deficit / Hyperactivity Disorder, or ADHD for short, and I often hear it used as a shorthand term for a person with that diagnosis.
Why's Johnny so hyper today?
Sorry I can't keep Johnny from screaming and running around the restaurant - he's ADHD.
Despite having grown up hearing (and sometimes using) hyper, I can't really recommend either of these - they're both extremely informal, and can be interpreted as either overindulgent of bad behavior OR dismissive of the victims of a serious condition. So be forewarned.
Peripatetic. This word could refer to someone who moves or walks about, or who does not stay in one place. I do not believe it implies necessity or compulsion to move.
Itinerant. This word is slightly more broad in definition than peripatetic. It refers to someone who moves from place to place. It may be more appropriate, depending on the context.
The technical term is akathisia defined as a state of motor restlessness ranging from an inner restlessness to an inability to sit still.
[from a- + -kithisia , ultimately from Greek cathedra seat]]
For more details see wikipedia