Is there any source which has the complete works of Abel, Lagrange, Jacobi and Gauss which has been translated into English? I'm asking for separate books for these mathematicians not necessarily a combined one for all of them.
"Complete works" usually refers to a collection of all author's publications and manuscripts, and that is almost never translated (one exception is Euler). Even individual books/papers are rarely translated from French or German into English, although some particularly famous ones were. For Abel see references under Where I can find the translated manuscript of Abel? Bruce made English translations of some Lagrange's papers, Gauss's Disquisitiones Arithmeticae is translated and so are General Investigations of Curved Surfaces of 1827 and 1825. See also relevant discussions on Principia generalia theoriae figurae fluidorum in statu aequilibri and Translations of Gauss' work on Gaussian integers. Also, Jacobi's Lectures on Dynamics were recently translated.
There are probably more, but they are not conveniently gathered in one place, you'd have to look case by case. Bruce did collect some of his translations of other mathematicians under Some Mathematical Works of the 17th & 18th Centuries, and the Euler Archive does translations methodically.
The simple answer is "no". They generally do not translate mathematical works from French and German to English, and rarely from Latin. Some separate works have been translated. For example Gauss, Disquisitiones generales circa superficies curvas, but very few of them. Much more is translated into European languages, for example into Russian, but even in Russian there are no translations of complete works of the mathematicians you listed.