Although many studies endorse the notion that the way students perceive support influences their engagement, very few have explored the possible mediator role of intention to learn between these variables. The present work provides new evidence to the existing literature because it analyses the work of intention to learn (measured with expectancy-value beliefs and achievement goals) as a mediating motivational variable in the relation between university students' external support (teacher and family) and their engagement. The Educational Situation Quality Model (MOCSE, its acronym in Spanish) has employed as a theoretical framework to perform this analysis. A sample of 267 Spanish university students completed the questionnaires employed to measure the considered variables at three times. They answered teacher and family support scales when the course began (time 1), intention to learn scales halfway through the course (time 2), and engagement scales when the course ended (time 3). The obtained structural equation models showed a positive and significant effect for teacher and family support on the considered motivational variables (expectancy-value beliefs and achievement goals) and these, in turn, on student behavioral engagement. These results allow us to point out a series of recommendations for university teachers to improve their students' involvement in their learning process.