The 62-year-old was questioned by police after clashing with his on-off girlfriend in the high street of Claygate, Esher, on December 2.
A Surrey Police spokesman said: “A 62-year-old man from Esher has been cautioned for common assault in connection with a domestic incident in Claygate high street on Wednesday, December 2.”
It is understood a passer-by dialled 999 as an argument took place between Wood and the 21-year-old Russian.
One resident described how she heard a woman screaming as a man pinned her to the ground. She said several people recognised the famous couple.
The arrest was one of the final chapters in a tumultuous relationship.