With sklearn you can have two approaches for linear regression:
LinearRegression object uses Ordinary Least Squares (OLS) solver from scipy, as Learning rate (LR) is one of two classifiers which have closed form solution. This is achieve by just inverting and multiplicating some matrices.
SGDRegressor which is an implementation of stochastic gradient descent, very generic one where you can choose your penalty terms. To obtain linear regression you choose loss to be
L2 and penalty also to
none (linear regression) or
L2 (Ridge regression)
There is no "typical gradient descent" because it is rarely used in practise. If you can decompose your loss function into additive terms, then stochastic approach is known to behave better (thus SGD) and if you can spare enough memory - OLS method is faster and easier (thus first solution).
This answer is mostly extracted from https://stackoverflow.com/questions/34469237/linear-regression-and-gradient-descent-in-scikit-learn-pandas/34470001#34470001
The OP @Netro is and the answer is from @lejlot