Can I ignore multicolinearity problem if all the regression coefficients are highly significant?
My data is large enough and all the resulting coefficients are significant enough in less than 0.01 level. The only thing I see is that one of the variable has the correlation of 0.9.
Can I keep this variable?
You probably meant that a $\textit{pair}$ of independent variables are highly correlated ($0.9$). Basically, although technically it's fine, this may indicate that both variables measure (almost) the same factor. Hence, generally speaking, bring the same information to the model, as such may cause redundancy. The fact that both variables are significant may be an artifact of the very large data set that you have. This is due to the fact that p.values are (generally) a monotone non decreasing (in most cases, strictly increasing) functions of the sample size.
Perhaps, if you want to keep both variables, you should consider to build one single index out of them.