To run multivariate regression use scipy.stats.linregress. Check out this nice example which has a good explanation.
The eliminateColinearAttributes option in the software you've mentioned is just some algorithm implemented in this software to fight the problem. Here, you need to implement some iterative algorithm yourself based on elimination of one of highly correlated variables with the highest p-value (then run regression again and repeat until multicollinearity is not there).
There's no one and only way here, there are different techniques. It is also a good practice to choose manually from the set of highly correlated with each other set of variables which to omit that it also makes sense.