We construct the sequences of Fibonacci and Lucas in any quadratic field $\mathbb{Q}(\sqrt{d}\,)$ with $d>0$ square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case $d = 5$, under the respective variants. For this construction, we use the fundamental unit of $\mathbb{Q}(\sqrt{d}\,)$ and then we observe the generalizations for any unit of $\mathbb{Q}(\sqrt{d}\,)$. Under certain conditions some of these constructions correspond to $k$-Fibonacci sequence for some $k\in \mathbb{N}$. Further, for both sequences, we obtain the generating function, Golden ratio, Binet's formula and some identities that they keep.